Detroit declined to trade up or down Thursday night, choosing Monroe to bolster its frontcourt.
Detroit finished last season 27-55 - its worst record since 1994 - and missed the playoffs for the first time since 2001.
The Pistons had a Top 10 pick for just the third time since Joe Dumars became president of basketball operations. The previous two were busts: Darko Milicic was drafted No. 2 overall in 2003, two years after Rodney White was taken ninth overall.