Republican Bundgaard's girlfriend, Aubry Ballard, 34, was booked for domestic violence assault, police said.
Phoenix police responded to a report on Friday night that Bundgaard was pulling Ballard out of a car stopped next to the median on State Route 51.
When officers arrived, they encountered Bundgaard and Ballard, and saw both had marks on their bodies showing they had been in a physical altercation, said Police Department spokesman Sgt. Tommy Thompson.
Bundgaard and Ballard were both detained, but Bundgaard told officers that under Arizona law he is immune from arrest while the legislature is in session, police said.
Police found Bundgaard could correctly claim immunity, but the case was submitted to prosecutors for review.
Bundgaard released a statement on Saturday saying he was innocent of wrongdoing. He said the physical altercation began when he had stopped the car, and his girlfriend moved into the driver's seat and refused to get out.
"I had no choice but to pull her from the driver's seat, which resulted in marks on her knees," Bundgaard said.
"I had also had no choice but to stop her from punching me and risking highway safety, all of which resulted in a black eye for me and a busted lip," he said.
He added, "I waive any and all 'legislative immunity.' If I did something wrong, charge me. I did not."
Bundgaard is the co-sponsor of controversial Arizona state legislation seeking to challenge the right to U.S. citizenship for children born in the state whose parents are illegal immigrants or other non-citizens.