NFL spokesman Greg Aiello tweeted Monday that there was no basis for a fine because the coaches didn't actually fight.
"However, both coaches told Ray Anderson today that their post-game conduct was wrong and will not happen again," Aiello wrote, referring to the NFL executive in charge of disciplinary matters.
"We believe their response is the correct one and that their post-game conduct going forward will be more appropriate."
Harbaugh shook Schwartz's hand and slapped him aggressively on the back after the 49ers pulled out a 25-19 victory.
Schwartz then chased Harbaugh down the field, yelling at him as a large group of players, coaches and officials gathered in a scrum near one of the end zones.
No punches were thrown and the coaches were mostly kept apart.
Schwartz said he was surprised by Harbaugh's use of an expletive, while the 49ers coach joked that he had shaken Schwartz's hand too hard.