Under the terms of the appointment, the banker will become chief operating officer at the brokerage unit this month - moving to chief executive in 2009.
Previously, Mr Mumma worked as the global head of derivatives trading at Bankers Trust, and at Nomura's global equity wing in the US.
The latest appointment marks the continuation of a recent trend at Mitsubishi, which has been looking to hire more non-Japanese personnel in order to gain greater international market intelligence.
One of the most high-profile moves has been that of Clifford De Souza to head up the firm's European investment banking and brokerage units in May.
Speaking to Bloomberg Susumu Taroura, a spokesman at Mitsubishi's brokerage unit, commented: "We're assigning personnel who are most conversant with the local market to top positions in Tokyo, London and New York.''
News of the appointment was originally reported in Japan's Nikkei newspaper earlier today.