Fury - who extended his unbeaten record to 32 wins and one draw - landed a right uppercut with just seconds left of the sixth round to earn victory.
The Gypsy King retained his WBC and Ring Magazine titles in the process - his second defence following victory over Deontay Wilder in October.
Whyte - who hit the canvas from the punch - rose to his legs but wobbled into the referee before hitting the ropes. Mark Lyson - the man in charge - halted the contest.
And a video appears to show a replay of the punch and before Whyte hits the canvas, his tooth appears to fly out.
When asked if he saw it himself, Fury said: "I didn't see, to be honest.
"I've given 20 years to boxing, amateur and professional," he said. "I've had my brains knocked about, been put down, dropped, cut, I've had tough fights, draws, wins, I've boxed all over the world," added Fury when asked if he would continue fighting.
"How much blood can you get out of a stone? I've given everything and put it on the line every single time and enough is enough. If it was about money I'd continue but it ain't about money, so I'm happy. It's never been about money, I'm not a money person. I know a lot of people who have money, big money, but none of them are happy, not one of them.
"Money cannot make happiness, it's not been about belts for me, it's not legacies, it's not been about anything apart from punching a motherfu***r's face in on the night. All I ever want to do is win."
Usyk - who holds the WBA, IBF, WBO and IBO belts - is reportedly in training for the fight and Saudi Arabia is favourite to host the fight.
Should Fury make a U-turn and decide to continue fighting, he could face the winner of Usyk-Joshua later this year to determine the first undisputed champion since Lennox Lewis.