The embattled Republican, cradling a basket of nachos, says to the fan "you're a big shot", their faces inches apart.
The drama unfolded during Sunday's Brewers v Cubs game in Milwaukee.
Mr Christie has the lowest approval ratings in the history of New Jersey, and stoked anger recently by using a beach closed to the public.
The baseball heckler, Brad Joseph, said that after Mr Christie walked past his seat, "I yelled his name and told him that he sucked".
"I called him a hypocrite because I thought it needed to be said," he added.
Chris Christie has gone from presidential timbre to political punching bag. Such is the tragic fate of the soon-to-be-former New Jersey governor.
It wasn't too long ago that Republican power brokers implored Mr Christie to be their white knight, riding into the Republican presidential nomination contest as Mitt Romney's campaign foundered.
At the time his in-your-face style seemed refreshingly candid and his popularity in Democratic-leaning New Jersey gave him cross-over national appeal.
Then the Bridgegate scandal - the pettiness of the apparent retribution scheme - tarnished his lustre. His idol, Bruce Springsteen, mocked him on late-night television. The media coverage grew more biting.
When Mr Christie eventually did try for the White House, Donald Trump had stolen his brash, unscripted thunder.
F Scott Fitzgerald once wrote that there are no second acts in American lives. That hardly seems the case these days, even for someone with Mr Christie's reputational scars.
He'll always have pugnacious attitude. Now, however, it's less a tool that will help him climb the political ladder than a bit of performance art for the entertainment of sports radio listeners and baseball spectators.
Earlier this month Mr Christie was booed by thousands of baseball fans at New York's Citi Field after he caught a foul ball that had landed in the stands.
Also this month, he clashed on live radio with one of his constituents whom he accused of being a "communist" and a "bum".
With a 15% approval rating, Mr Christie is considered to be one the least popular state governors in American history.
Once a contender for the White House, his popularity has plunged after the so-called Bridgegate scandal in which his senior aides were convicted of conspiring to close one of the busiest bridges in the world as political payback against a mayor that refused to endorse Mr Christie.
New Jersey Governor Chris Christie has angrily confronted a heckler during a baseball game in Wisconsin.