Donnarumma was left requiring 10 staples after suffering lacerations to the right side of his face when he was caught by the studs of Singo during PSG's 4-2 win in the principality on Wednesday.
"I'd like to apologise to Gianluigi Donnarumma. My act was obviously not intentional, but I was able to see afterwards that he had a serious injury to his face," Singo wrote on Instagram.
He then addressed the shotstopper directly, saying "I wish you a good recovery".
Donnarumma was unable to continue after the challenge early in the match and was replaced by Matvey Safonov.
He will undergo "medical examinations on Thursday and will have to remain inactive for several days", a statement from PSG said.
Footage published by PSG showed the two players greeting each other in the stadium after the final whistle, with the Italian telling the Ivorian: "Everything's fine, no worries."
Singo, already on a booking, did not receive a red or yellow card for the challenge, which the referee adjudged to have been "part of the action", according to PSG captain Marquinhos.
Monaco announced Thursday that the defender has been subject to racist insults on social media in the aftermath of the incident.
"(Monaco condemns) in the strongest possible terms the unacceptable racist comments made about Wilfried Singo on social media after the match," the club said in a statement.
"Such behaviour has no place in sport, either on or off the pitch, and is totally at odds with the values that the club stands for."
© 2024 AFP