In footage widely shared on social media, Mourinho appears to reach out from behind his opponent and make contact with his nose after a fiery match on Wednesday. Buruk then falls to the ground holding his face before Mourinho is escorted away.
Three players were sent off in the Istanbul derby at Fenerbahce's stadium, which Galatasary won 2-1.
"He squeezed my nose from behind while I was going on. There was a slight scratch. Of course, it's not a very nice and stylish thing," Buruk said after the quarter-final match.
"I won't exaggerate about it, but it's not a very stylish thing."
Galatasaray vice president Metin Ozturk was not so restrained in his response to a fresh controversy involving the outspoken Mourinho.
"The latest incident is not only an attack on Galatasaray's coach but also on Turkish football. This is Mourinho, I don't know where he gets this courage," he said.
"Where in the world can he do this? Where does he think Turkey is?"
Mourinho was accused by Galatasaray in February of making racist comments after another match involving the Istanbul rivals. Galatasaray said the former Real Madrid, Manchester United and Chelsea manager had used "unequivocally inhumane rhetoric" after he referred to the opposition bench "jumping around like monkeys."
Fenerbahce rejected the accusation and then said it had filed a lawsuit against Galatasaray for an "attack on the personal rights" of Mourinho.
Galatasaray reveled in their victory on Wednesday and posted a picture on its official X account of a smiling Buruk looking in Mourinho's direction.
"YOU SHOULD NOT ATTACK, YOU SHOULD DIGEST!" was the message accompanying the picture along with a shushing emoji.
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