Schweinsteiger, who is currently on holiday following the World Cup, sang a popular song among fans in a Munich bar. The video was then published on the internet, prompting an immediate apology from the Germany international.
"I would like to apologise for this," he said on Facebook. "Of course I don't want to make anything out to be better than it actually is, it was only a well-known fans' song, although I didn't mean to insult anybody with the swear word.
"I get on well with all of Dortmund's players, particularly with Kevin Grosskreutz. It was just an unfortunate situation."
Schweinsteiger's apology has already been accepted by defender Grosskreutz, who replied on his own Facebook account.
"It wasn't a cool thing to do, but I can understand his explanation and I'm never going to forget all of the good things he's done for me," he said.