Following the red card, Tosic had to be held back by his team-mates as he tried to engage van Persie before leaving the field.
Fenerbahce went on to win 1-0 thanks to a late goal from the Netherlands international, sending them in to the last eight of the Turkish Cup.
After the game, Jelena Karleusa posted a strongly worded message on Twitter defending her husband and attacking Van Persie, writing "R. van Persie is one stupid motherf**ker. Brake a leg asshole!"
Karlesusa is a successful Serbian pop star, and has sold millions of albums in the Balkans, while Tosic is a former QPR defender who has 19 caps for his national side.