The game between the Buffalo Bills and the Cincinnati Bengals that was suspended Monday night after the Bills’ Damar Hamlin collapsed on the field will not be completed, the N.F.L. announced Thursday. N.F.L. Commissioner Roger Goodell called the decision to cancel the game “difficult, but necessary” under the “extraordinary circumstances.”

Hamlin, a 24-year-old starting safety for Buffalo, went into cardiac arrest after making what appeared to be a routine tackle during the first quarter Monday. Hamlin was still in critical condition, but the doctors treating him at a Cincinnati hospital said on Thursday that Hamlin was awake and able to communicate in writing.

On Monday night, medical professionals worked on Hamlin for several minutes to restore his heartbeat on the field. After he was taken away in an ambulance, Bengals Coach Zac Taylor crossed the field to confer with Bills Coach Sean McDermott and the game officials.

Taylor later said that McDermott had told him, “I need to be at the hospital for Damar, and I shouldn’t be coaching this game.” The players from both teams headed back to their locker rooms, and at around 10 p.m. — about an hour after Hamlin collapsed — the game was suspended.

The N.F.L. had said on Tuesday that the game would not be resumed this week but that it had not made a decision on when or whether it would be rescheduled.

The game was stopped nine minutes into play, with the Bengals leading, 7-3, and would have had implications for postseason seeding in the A.F.C. Both teams, along with Kansas City (13-3), were vying for the No. 1 seed, which comes with a first-round bye and home-field advantage.

With the game’s cancellation, the Bills (12-3) and Bengals (11-4) will each have played one fewer game than the other teams in the N.F.L. when the regular season concludes after this weekend’s games. This will not change which teams make the playoffs in their conference but may affect how they are seeded.

To address potential competitive discrepancies, the league’s 32 clubs will meet on Friday to consider a resolution with two adjustments to the A.F.C. playoffs that were recommended by Goodell and approved by the competition committee.

First, the A.F.C. Championship Game would be held at a neutral site if the teams that qualify played an unequal number of games and both could have been the top seed if all games had been completed. Second, if the Baltimore Ravens (10-6) beat Cincinnati for the second time this season on Sunday, and if the A.F.C. North rivals are scheduled to play one another in the wild-card round, the game site would be determined by a coin toss.

“As we considered the football schedule, our principles have been to limit disruption across the league and minimize competitive inequities,” Goodell said in a statement. “I recognize that there is no perfect solution. The proposal we are asking the ownership to consider, however, addresses the most significant potential equitable issues.”

When the N.F.L. played the 2020 season in the first year of the coronavirus pandemic, clubs understood there was a possibility that some games could be canceled and they might have to accept uneven standings because of the circumstances. That did not happen, because the N.F.L. played a complete schedule that season. But this is a concept teams have contemplated before, and they are likely to go along with these changes given the gravity of this week’s events.

“This has been a very difficult week,” Goodell said. “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.”