The Iron Man 2 actress went public with her new relationship at the second season premiere of Kinnaman's TV hit The Killing in Los Angeles on Monday (26Mar12).
Munn is said to have begun her romance with Swedish-born Kinnaman, who will play the title role in the upcoming Robocop reboot, after they met last year (11).
A source tells EOnline.com, "They have been together for about three months. They met last year, but they didn't get together until just before Christmas.
"He is a super normal guy and she is a really down-to-earth girl and they just get each other. They are on the same wavelength intellectually, and they have the same sense of humour. It's been going on for a little while and it's heading towards being serious. They are extremely happy together."
Before dating New York Rangers ice hockey star Richards, Munn was linked to Justin Timberlake, Chris Pine and Matthew Morrison.