Cheik Modibo Diarra was detained on Monday at his home in the capital Bamako, reportedly on the orders of the coup leader, Capt Amadou Sanogo.
He had been due to travel to France.
Mr Diarra was made prime minister of an interim government in April after the military officially handed power back to civilians.
The 60-year-old astrophysicist has backed plans to send a West African intervention force into the northern half of Mali which was seized after the coup by Islamists and Tuareg separatists.
But tensions between the soldiers who led the coup and the civilian prime minister they were forced to appoint have been mounting in recent weeks.
Many within Mali's military are opposed to foreign intervention, saying they need only financial and logistical support.
Military spokesman Bakary Mariko told the BBC that the prime minister was suspected of attempting to jeopardise the planned political dialogue over the transition to democracy.
"Eight months ago the prime minister was given the mission to help Mali recover its territorial integrity, but unfortunately he has been working to stay in power indefinitely," he said.
Mr Diarra would be held until a new prime minister was appointed by the interim president, the spokesman said.
'Hope for peace'
In his address on national broadcaster ORTM, Mr Diarra gave no clear explanation of his resignation.
"Men and women who are worried about the future of our nation, you are hoping for peace. It's for this reason that I, Cheikh Modibo Diarra, am resigning along with my entire government."
A member of the president's entourage earlier told AFP news agency that the prime minister had been arrested by about 20 soldiers from the sprawling Kati military base where the 21 March coup was launched.
The source said soldiers had: "smashed in the door of the prime minister's residence and took him away a bit violently".
"They said Captain Sanogo sent them to arrest him," he added.
Security officials said Mr Diarra was then driven to Kati.
The military spokesman told Reuters that Mr Diarra "wanted to leave the country having incited trouble".
The prime minister had been about to leave the country for France - the spokesman told the BBC he had been due to have a medical check-up there. It is not known if he had been trying flee.
The streets of Bamako were reported to be quiet early on Tuesday. One reporter told the BBC that "people were starting to go to work and maybe did not get the information yet".
'Potentially explosive'
Mr Diarra, the son-in-law of Moussa Traore, a former Malian coup leader and president, had been leading a government of national unity.
It was formed in August in an attempt to satisfy regional demands for a transition from military rule and to restore stability following the March coup, which led to the entire northern half of the country being occupied by hardline Islamists and Tuareg rebels.
The Islamists have since taken control of northern Mali's main urban centres, imposing a strict version of Islamic law.
The United Nations warned on Monday that the north of the country is now "one of the potentially most explosive corners of the world".
The West African regional group Ecowas has agreed to send 3.300 troops to reclaim rebel-held territory. The deployment has been backed by UN Secretary General Ban Ki-moon.
On Monday, the European Union backed plans for a 250-member training mission for around four battalions of the Malian army to fight the militants.



Source: bbc.co.uk

thiendella: Cheik Modibo Diarra was detained on Monday at his home in the capital Bamako, reportedly on the orders of the coup leader, Capt Amadou Sanogo.
He had been due to travel to France.
Mr Diarra was made prime minister of an interim government in April after the military officially handed power back to civilians.
The 60-year-old astrophysicist has backed plans to send a West African intervention force into the northern half of Mali which was seized after the coup by Islamists and Tuareg separatists.
But tensions between the soldiers who led the coup and the civilian prime minister they were forced to appoint have been mounting in recent weeks.
Many within Mali's military are opposed to foreign intervention, saying they need only financial and logistical support.
Military spokesman Bakary Mariko told the BBC that the prime minister was suspected of attempting to jeopardise the planned political dialogue over the transition to democracy.
"Eight months ago the prime minister was given the mission to help Mali recover its territorial integrity, but unfortunately he has been working to stay in power indefinitely," he said.
Mr Diarra would be held until a new prime minister was appointed by the interim president, the spokesman said.
'Hope for peace'
In his address on national broadcaster ORTM, Mr Diarra gave no clear explanation of his resignation.
"Men and women who are worried about the future of our nation, you are hoping for peace. It's for this reason that I, Cheikh Modibo Diarra, am resigning along with my entire government."
A member of the president's entourage earlier told AFP news agency that the prime minister had been arrested by about 20 soldiers from the sprawling Kati military base where the 21 March coup was launched.
The source said soldiers had: "smashed in the door of the prime minister's residence and took him away a bit violently".
"They said Captain Sanogo sent them to arrest him," he added.
Security officials said Mr Diarra was then driven to Kati.
The military spokesman told Reuters that Mr Diarra "wanted to leave the country having incited trouble".
The prime minister had been about to leave the country for France - the spokesman told the BBC he had been due to have a medical check-up there. It is not known if he had been trying flee.
The streets of Bamako were reported to be quiet early on Tuesday. One reporter told the BBC that "people were starting to go to work and maybe did not get the information yet".
'Potentially explosive'
Mr Diarra, the son-in-law of Moussa Traore, a former Malian coup leader and president, had been leading a government of national unity.
It was formed in August in an attempt to satisfy regional demands for a transition from military rule and to restore stability following the March coup, which led to the entire northern half of the country being occupied by hardline Islamists and Tuareg rebels.
The Islamists have since taken control of northern Mali's main urban centres, imposing a strict version of Islamic law.
The United Nations warned on Monday that the north of the country is now "one of the potentially most explosive corners of the world".
The West African regional group Ecowas has agreed to send 3.300 troops to reclaim rebel-held territory. The deployment has been backed by UN Secretary General Ban Ki-moon.
On Monday, the European Union backed plans for a 250-member training mission for around four battalions of the Malian army to fight the militants.



Source: bbc.co.uk

Thanks for this news, I have been following this closely.

Ur welcome

https://www.youtube.com/watch?v=FXeE1tn8gZ8&feature=youtube_gdata_player

Modibo Diarra is back on Earth, he learned that politics is not Nasa.
How can a rocket scientist like him not be unable to raise funds and a push for an african space program?
Welcome back to planet Earth ,dummy !