The answer is no, NFL spokesman Greg Aiello said in a statement released to NFL Network insider Jason La Canfora on Monday.
"Fortunately, there was no fighting and thus no basis for a fine," Aiello said. "However, both coaches told (NFL vice president of football operations) Ray Anderson today that their postgame conduct was wrong and will not happen again. We believe their response is the correct one and that their postgame conduct going forward will be more appropriate."
NFL.com senior writer Steve Wyche cited a league official in reporting that Harbaugh and Schwartz received written warnings, which is considered a strike against them in case any other infractions arise in the future.
On Monday, neither coach offered an apology for his actions.
"Personally I can get better at the postgame handshake, and we'll attempt to do that," Harbaugh said. "I don't think that there's any reason for an apology. We spoke about it after the game, and at some point, we will talk in private. Apologies always seem to me like excuses."
Harbaugh and Schwartz said they briefly spoke in the tunnel at Ford Field following the altercation. One sentiment they share is they don't like that their confrontation has stolen the thunder from one of Sunday's marquee matchups.
"I think that it is unfortunate that the events after the game have overshadowed the fact that it was probably one of the better games played yesterday," Schwartz said. "It's unfortunate. The game's played by the players on the field, and you certainly don't want things like that to occur, but there's competitive people in the league. That said, we need to do a better job of just leaving it to the players on the field."
Said Harbaugh: "It was an unfortunate incident that took place after the game. I take accountability and responsibility for my part in that. The thing that you feel bad about is that it detracts, takes away from what our football players did, what their football players did, and the game itself."
Specualtion has been that Harbaugh's forceful handshake might have been a delayed reaction to that, but Schwartz said he doubts it played any role in what happened after the game.
"I don't think he was watching on TV, and you can't hear things across the field," Schwartz said. "You can't challenge a scoring play."
Asked if Schwartz did anything wrong, Harbaugh took the high road.
"We're not here today to throw any salvos. There's not going to be any salvos coming out of the West Coast," Harbaugh said. "I have a lot of respect for Jim and the Detroit Lions. ... It was great competition. It was rough, hard football."
The Associated Press contributed to this report.