"Michael, you can't do that," Dungy said to SI.com.
Vick was seen in the recent New York Post photo drinking vodka and pineapple juice.
It wasn't immediately clear when the photo was published whether Vick was violating conditions mandated by NFL commissioner Roger Goodell.
In a letter to Vick upon his reinstatement July 27, after a two-year prison sentence for his participation in a dogfighting ring, Goodell wrote that "prohibitions regarding drug and alcohol use" were included.
But an Eagles spokesman, in an e-mail to The Philadelphia Inquirer, confirmed it was OK for Vick to drink alcohol, that it was "not in conflict with terms of his probation or reinstatement with the NFL."