In addition, the league fined each coach's team $250,000, sources said.
The $1,050,000 in punishments comes a week after the league sent a memo to teams reinforcing its requirement that coaches wear coverings over their mouths and noses at all times on the sidelines during games, threatening discipline for those who don't comply.
The sharply worded message, written by executive vice president of football operations Troy Vincent, came in response to wide variance in compliance during the first Sunday of the 2020 season.
Players are exempt from these protocols.
More fines could be coming, as several other coaches violated the league's rules, among them New England Patriots coach Bill Belichick and both coaches in Monday night's game, Jon Gruden of the Las Vegas Raiders and Sean Payton of the New Orleans Saints.
Gruden wore his face mask like a chin strap and Payton wore his gaiter like a turtleneck.
Following the Raiders' 34-24 win over the Saints on Monday night, Gruden, who last week said he felt the league's memo was directed at him, revealed he'd had COVID-19 and apologized for violating the rules.
"I'm doing my best," Gruden said. "I've had the virus. I'm doing my best. I'm very sensitive about it ... I'm calling plays. I just wanna communicate in these situations, and if I get fined, I'll have to pay the fine, but I'm very sensitive about that and I apologize."
The Associated Press contributed to this report.