After All-Star Harper flied out in the eighth inning, he returned to the dugout and started exchanging words with veteran Papelbon.
The verbal spat quickly became heated and then Papelbon went for Harper's throat with his left hand and slammed him against the wall.
Team mates and manager Matt Williams quickly separated the pair.
"I'm in the wrong there ... I've talked to Bryce and told him how we feel. We're on the same page now," Papelbon, a six-time All-Star, told reporters.
Harper, who is regarded as a contender for the National League's most valuable player, was clearly upset by the incident.
"He apologized. Whatever, I really don't care," he said.
Papelbon going after Harper 👀 pic.twitter.com/Cxqmj0l4Xq— Baseball Vines™ (@BsbVines) September 27, 2015
Manager Williams said the altercation came "out of the blue" and that Papelbon had been suspended.
"Certainly, there's a lot of testosterone flowing among young men competing," Williams said.
"This is a family issue and we'll deal with it that way."
The fight occurred just one week before the Nationals complete a disappointing season.
They were widely expected to make the playoffs, but have fallen out of playoff contention and have a 79-76 record after losing to the Phillies 12-5 on Sunday.
Papelbon took the loss after giving up five runs in one inning.