TMZ posted video showing Ariel Ramirez punching Fieri through the open door of an SUV, then Fieri kicking Ramirez, while both scream expletives at each other.
The celebrity news website said the clip doesn't show how the fracas ends, but quotes unnamed sources as saying Fieri threw Ramirez out of the vehicle after which Fieri's manager took Ramirez home by cab.
TMZ said the trio had been drinking on their flight to San Francisco.
"A bunch of guys were messing around. Things got a little out of hand, but they're all good now," Fieri's representative told the celebrity news website.