Bomar, 26, was booked about 5:15 a.m. Sunday for third-degree driving while intoxicated, Blue Earth County Jail spokeswoman Amber Carlson said.
Vikings head coach Leslie Frazier said Bomar addressed the team prior to practice Monday morning at Minnesota State University and apologized for his actions.
"It's not something we're pleased with. We think we can handle it internally," Frazier said. "Hopefully, he can learn from this mistake and move forward."
Bomar declined to comment specifically on what he said to the team after practice.
"I'm keeping (the apology) within the team," Bomar said. "I wanted to get up there and say something to them, and coach gave me the opportunity."
The Vikings signed Bomar last December from the New York Giants practice squad. He was a fifth-round draft pick in 2009 out of Sam Houston State. Bomar is a long shot to make the team, fourth on the depth chart behind veteran Donovan McNabb, first-round draft pick Christian Ponder and second-year man Joe Webb.