Cellphone video, taken by WISN-TV reporter Ben Hutchison, captured the confrontation inside Miller Park. Hutchison tweeted the video Sunday afternoon.
The incident started when Cubs fan Brad Joseph yelled at the governor as he passed him, telling him that "he sucked" and calling him a "hypocrite," he told WISN-TV.
Christie, whose son works for the Milwaukee Brewers, turned around and got into Joseph's face. In the video, Christie -- while holding a plate of nachos -- is heard saying "you're a big shot" and then walks away. Joseph responds "I appreciate that."
Joseph told WISN-TV: ""When he initially was going up the stairs I yelled his name. He was quite a bit past me, and 30 feet away I yelled his name and told him that he sucked. ... I called him a hypocrite because I thought it needed to be said. He turned around back towards me and got in my face for what seemed like a long time, but was probably only about 30 seconds or a minute. (He) was yelling at me. First he told me, 'Why don't you have another beer?' which I thought was a decent come back, and I thought that was kind of funny. Then he started calling me a tough guy."
As for the game, the Cubs beat the Brewers, 4-2.
On July 18, Christie was loudly booed at Citi Field in New York after snagging a foul ball during a game between the St. Louis Cardinals and Mets.
The Republican governor's approval ratings are hovering in the mid-teens, making him the least popular governor in New Jersey history.