The outcome of the game would have affected the play-off seedings so the NFL is considering staging the AFC Championship game at a neutral venue.
There is just one round of games left in the regular season, to be played this weekend, with the play-offs set to start on 14 January.
Not playing the Cincinnati-Buffalo game to its conclusion has no effect on which clubs qualify for the post-season, with both teams already assured of being among the top seeds from the AFC Conference.
However, an NFL statement says it creates “potential competitive inequities” through the play-offs as both teams will have played a game fewer than their rivals and a team’s record determines who has home advantage.
The team with the best record in a Conference also receives a bye in the first round of the play-offs. In the AFC, the top seeding is between the Bills, the Bengals and the Kansas City Chiefs.
The NFL commissioner, Roger Goodell, and the competition committee have recommended playing the AFC Championship game at a neutral stadium if the participating teams have played an unequal number of games.
The winner of that game, scheduled for 29 January, will represent the AFC in Super Bowl 57 on 12 February.
“Our principles have been to limit disruption across the league and minimise competitive inequities,” said Goodell. “I recognise that there is no perfect solution.”
NFL clubs will consider the recommendation at a special league meeting on Friday, which Goodell says “addresses the most significant potential equitable issues created by the difficult, but necessary, decision not to play the game under these extraordinary circumstances”.
‘I’m kind of glad that we chose not to play’
Hamlin has been in an intensive care unit since collapsing during Monday’s game, causing an outpouring of support from fans.
He is still on a ventilator at the University of Cincinnati Medical Center but has been communicating with doctors and on Thursday they said he “appears to be neurologically intact”.
Hamlin collapsed after colliding with Bengals wide receiver Tee Higgins, who said the days since the incident have “been hard”.
“Everybody’s been making me feel whole again,” he added. “I talked to his mom. He’s doing good, so I’m in a good place right now.
“[She was] telling me that she’s thinking of me, praying for me, that he’s OK.”
On seeing Hamlin collapse after the tackle, Higgins added: “I knew it was something crazy, something tragic. Man, it was hard. Obviously, wasn’t in a good place to play for the rest of that game, so I’m kind of glad that we chose not to play.”
Goodell told all clubs on Thursday that the game had been cancelled, after speaking with the Bills, the Bengals and the NFL Players Association.
“This has been a very difficult week,” he added.
“We continue to focus on the recovery of Damar Hamlin and are encouraged by the improvements in his condition as well as the tremendous outpouring of support and care for Damar and his family from across the country.”