Kaltenborn was born in Dehradun, India. Her family emigrated to Vienna when she was a child and she subsequently took Austrian citizenship. Between 1990 and 1995 she studied for a law degree at the University of Vienna. She then pursued further education at the London School of Economics and was awarded a master's degree in International Business Law from the University of London in 1996.
During her student years in Vienna she gained early professional experience working for the United Nations Industrial Development Organization and the UN Commission for International Trade Law.
After completing her studies, Kaltenborn worked at several legal firms: first in Stuttgart with Gleiss Lutz, then back in Vienna with Wolf & Theis, and finally for the Fritz Kaiser Group between 1998 and 1999. Kaiser was at that time a co-owner of the Sauber Formula One team, alongside founder and team principal Peter Sauber and Red Bull owner Dietrich Mateschitz. Through the Kaiser Group, Kaltenborn was employed to take charge of Sauber's corporate and legal affairs.
When Kaiser sold his shares in 2000, Kaltenborn remained with the team as head of its legal department. From 2001 she served as a member of Sauber's management board, progressively extending her influence over the team's operations.
In early 2010, following the withdrawal of BMW as a partner and the team's return to independent status, Kaltenborn was appointed chief executive officer of Sauber Motorsport AG. She also became involved in the FIA's Commission for Women and Motorsport, chaired by Michèle Mouton.
On 16 May 2012, Peter Sauber transferred one third of the Sauber team to Kaltenborn, making her a part owner. In October of that year, Peter Sauber retired from front-line management of the team and handed her the role of team principal — the first time in Formula One that a woman had held that position.
On 22 June 2017, the Sauber F1 Team confirmed that Kaltenborn would be leaving the Sauber Group with immediate effect. The statement from Longbow Finance SA, which had taken over the team in July 2016, cited diverging views on the future of the company: "Longbow Finance SA regrets to announce that, by mutual consent and due to diverging views of the future of the company, Monisha Kaltenborn will leave her positions with the Sauber Group effective immediately."
In February 2018, Kaltenborn returned to motorsport with the founding of KDC Racing. The team was a fifty-fifty venture between Kaltenborn — whose initial provides the K in the team name — and French-Monegasque businesswoman Emily di Comberti, whose son Aaron had competed in the BRDC British Formula 3 Championship in 2017. KDC Racing made its competitive debut in the Italian and ADAC Formula 4 championships.
Kaltenborn met her husband Jens Kaltenborn during her first job in Stuttgart and later married him in Dehradun.