The Cleveland Browns have seen their share of highs and lows over the decades, including the past 17 years, when they won less than one-third of their games and failed to reach the playoffs.

Misery turned to elation on Sunday, though, when the Browns beat the Pittsburgh Steelers to qualify for the postseason for the first time since the 2002 season and end the N.F.L.’s longest playoff drought.

The Browns’ championship aspirations took a severe hit on Tuesday when the team said its head coach, Kevin Stefanski, two other coaches and two players tested positive for the coronavirus, the latest additions to a growing outbreak that has hampered the team the last few games.

All five people will miss the Browns’ matchup against the Steelers on Sunday night in Pittsburgh. Special teams coordinator Mike Priefer will take over as head coach in Stefanski’s absence. The Browns have shut their training facility in Berea, Ohio, in the meantime.

Offensive lineman Joel Bitonio is one of the two players who tested positive. Bitonio has been with the Browns his entire seven-year career, which has included the 2016 and 2017 seasons, when the team went 1-15 and 0-16.

Stefanski gave Bitonio, the longest tenured player on the team, the game ball after Sunday’s win. Now Bitonio will miss his first chance to play in a postseason game.

“This is just a terrible scenario for him,” J.C. Tretter, a center on the Browns and the president of the N.F.L. Players Association, said after the team’s announcement.

The number of players, coaches and staff who tested positive picked up noticeably starting in November as the virus raged through communities around the country.

In the week that ended Jan. 2, the N.F.L. said there were 34 new confirmed positive tests among players and 36 new confirmed positives among other personnel. The 70 combined cases was up from 58 positive tests the week before and 45 cases the week before that.

Since August, 256 players and 432 coaches and staff have tested positive for the virus. There are at least 6,000 people regularly being tested throughout the league, including about 2,500 players on rosters and practice squads.

During the season, outbreaks on the Tennessee Titans and Baltimore Ravens forced the league to postpone games and shuffle schedules, including games that involved the Steelers. But the N.F.L. said the status of the Browns-Steelers game on Sunday had not changed. Bye weeks during the regular season gave the league room to move games, but there are no bye weeks in the playoffs.

“Given the schedule we have now, we may not have the same flexibility that we had in the regular season,” said DeMaurice Smith, the executive director of the N.F.L. Players Association.

In the meantime, the league and team will continue “to conduct standard contact tracing to identify any possible high-risk close contacts,” according to a statement from the league.

“We obviously have more work to do with contact tracing and figuring out where the virus is coming from,” Tretter said. “We don’t have all the answers yet.”

Stefanski and the other coaches and players must be isolated from the team for a minimum of 10 days. If any players or other staffers are found to have had close contact with them, they would need to remain apart from the team for five days, after which they would be eligible to return to the team and play in the game.

During their 24-22 victory over the Steelers, the Browns had six players on the Covid-19 reserve list who had either tested positive or had close contact with someone who had. The previous week, the Browns had played without any of their best wide receivers because of an outbreak on the team.

Stefanski, 38, is in his first year as Cleveland’s coach. He is the 11th coach to lead the Browns since their last visit to the playoffs. He led the team to an 11-5 record, the Browns’ best regular-season finish since the 1994 season, when Bill Belichick was the coach.

That team was also the last Browns squad to win a playoff game. They defeated the New England Patriots in the wild-card round before the Steelers ended their season the following weekend.