The incident followed San Francisco's 25-19 victory over the Lions Sunday during which Harbaugh shook Schwartz's hand following the game but then slapped him aggressively on the back.
Schwartz responded by chasing Harbaugh down the field and yelling at him as a group of players, officials and other coaches milled about near an end zone.
NFL spokesman Greg Aiello indicated in a Twitter posting Monday no fines would be assessed because the two didn't come to blows.
"However, both coaches told [NFL discipline chief] Ray Anderson today that their post-game conduct was wrong and will not happen again," Aiello wrote.
"We believe their response is the correct one and that their post-game conduct going forward will be more appropriate."
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
Duggar sisters unveil Christian dating rules in new book