Kaltenborn, 41, already held the role of chief executive officer and will immediately take on the additional responsibilities at this weekend's Korean Grand Prix as 68-year-old Sauber takes a back seat.
The move had appeared on the cards when Sauber transferred a third of the team's equity to Kaltenborn as a 'gift' at the end of 2011.
In a team statement, Sauber said: 'We decided a long time ago that Monisha would take over from me, 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.
Over to you: Peter Sauber is taking a step back
Sauber, who first entered F1 in 1993, have enjoyed an encouraging campaign. The Swiss team lie sixth in the constructors' championship after scoring four podium finishes, the most recent at last weekend's Japanese Grand Prix through Kamui Kobayashi.
Indian-born Kaltenborn, who holds Austrian citizenship, initially joined Sauber in 2000 to run their legal department but had moved up to the role of CEO in January 2010.
She said: 'I have set my sights high and am committed to taking the team forward as Peter Sauber would want and leading it on to success.'
Podium finish: Kobayashi came third in the recent race in his native Japan