She will share her responsibilities with the managing director, Richard Alford.
The appointment comes as the agency looks to broaden its services.
Tim Duffy, the M&C chief executive, said: "Carrie is a leader. Not only has she got a great track record of creative work, she has the knowledge and enthusiasm to guide clients through the new-media landscape. She will drive the agency forward."
Over the past year, Hindmarsh has been responsible for a restructure within M&C that involved retraining account handlers as project managers to promote a multi-discipline approach to briefs.
Duffy added: "With 90 per cent of our clients working with us across disciplines beyond advertising and 15 per cent of UK group revenues now coming from digital, Carrie will be driving significant change in the agency."
Hindmarsh was a founding member of M&C and has run accounts such as Transport for London. She became the deputy managing director in April 2005.
The news comes as M&C picks up the £1 million launch project for the US-based website Seatwave.com which allows people to buy and sell tickets directly, instead of using touts or auction sites.