Fenerbahce said in a statement that Mourinho was suing Galatasaray for 1,907,000 Turkish lira ($52,223) due to "the attack on the personal rights" of the Portuguese coach.
While Fenerbahce did not provide further details, the lawsuit follows Monday's Istanbul derby between the two clubs.
After the game, which ended in a 0-0 draw, Galatasaray accused Mourinho of making racist statements and said they would initiate criminal proceedings against the Portuguese manager.
Mourinho said in a post-match press conference that the home side's bench had been "jumping like monkeys" and that the match would have been a disaster if a Turkish referee had been in charge.
Mourinho received a four-match ban from the Turkish Football Federation (TFF) for his comments.
The TFF cited "derogatory and offensive statements" and accusations of chaos in Turkish football.
When contacted by Reuters, a Galatasaray spokesperson said they had already sued Mourinho and had no further comment.