Passmore grew up in Wynnum-Manly, Brisbane. In the early 1990s, he served in the army, followed by a variety of jobs, including factory work, before eventually moving to Sydney to attend the National Institute of Dramatic Art (NIDA) in 1999. He graduated in 2001.

Passmore married PR guru Jacqui Passmore in 1997. Following the end of their marriage in 2006, Matt met girlfriend Rachael Carpani on the set of McLeod's Daughters when he returned to play Marcus, Alex's brother. They ended their relationship in 2011.

Passmore has an older brother and a younger sister.

Passmore began his career on the children's television series Play School.

Later on, he took on a variety of roles on Australian television shows such as Always Greener, Blue Heelers, The Cooks, Last Man Standing, McLeod's Daughters, and Underbelly: Tale of Two Cities.

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