Juventus, European champions in 1985 and 1996, lost the final to Barcelona in 2015 but defeated Luis Enrique's side 3-0 on aggregate in this year's quarterfinals.
Monaco have only once reached the final, losing to Jose Mourinho's Porto in 2004. They eliminated Manchester City and Borussia Dortmund on their way to the last four.
Juventus director Pavel Nedved said the club could go all the way but warned that semifinal opponents Monaco would pose a tough challenge.
Meanwhile, Monaco vice president Vadim Vasilyev said his side had the chance to gain revenge for their defeat to the same club in the 2015 quarterfinals.