A native of Johnson City, NY, Dunham played college hockey for the University of Maine. The team won the NCAA Men's Ice Hockey Championship in Dunham's final season, 1992–93.
Internationally, Dunham played for the USA Hockey National Junior team in 1991 and 1992 and the USA Hockey Men’s National Team in 1992, 1993, 1998, and 2004. He was a member of the 1992, 1994 and 2002 USA Men’s Olympic team winning a Silver Medal in 2002.
He was drafted in the 3rd round (53rd overall) of the 1990 NHL Entry Draft by the New Jersey Devils. He won the Calder Cup in 1995 with the Albany River Rats. He also won the William M. Jennings Trophy with Martin Brodeur after the 1996–97 NHL season. During the 1998 expansion draft, Mike Dunham was selected by the Nashville Predators where he played four seasons. He also played for the New York Rangers, Atlanta Thrashers, and New York Islanders.