Gronkowski was penalized in the fourth quarter of New England's 23-3 win over the Bills on Sunday.
After White intercepted a pass by Patriots quarterback Tom Brady that was intended for Gronkowski, he rolled out of bounds. Gronkowski then dove on him, driving his shoulder into the back of White's helmet.
"I don't believe in shots like that," Gronkowski said after the game (via ESPN.com's Mike Rodak). "I'm not in the business of that. It was a lot of frustration. At that moment, it happened naturally through emotions and frustration."
Officials flagged Gronkowski for unnecessary roughness. White was placed in the NFL's concussion protocol after the hit.
Gronkowski leads the Patriots in targets (85), receptions (55) and receiving touchdowns (seven) this season.