The 41-year-old becomes the first female to do such a job in Formula 1 but Sauber has revealed that he has great faith in his replacement.
"We decided a long time ago that Monisha would take over from me," Sauber said. "But we left the timing open. Now is a good time for both of us, so this is the right moment to pass on the baton.
"After all, there have been a number of races I've been unable to attend - most recently the Japanese Grand Prix, where the team put in an excellent performance."
Sauber will remain president of the board following the decision to step down from his role in the team.