Cherif Traore (28), who also represents Italy at national level, wrote on Instagram on Wednesday that some players had laughed when he opened the present. He later said he had accepted an apology for what happened.
His club issued two statements on the issue on Wednesday, but made no suggestion they planned to investigate the incident or take action against the player responsible.
In a change of tone on Thursday, they issued a third statement saying the national sports prosecutors' office would look into what had happened "in order to protect the founding values and reputation of the game".
It added: "At the same time, Benetton Rugby has decided to suspend as a precautionary measure, for the entire duration of the investigations by the prosecutors, one of its own players."
They did not name the player.
Benetton Treviso said it would be up to federal investigators to impose any sporting or administrative sanctions.
Traore was born in Guinea but has lived in Italy since the age of seven. He wrote on Instagram that he did not normally react to "racist jokes" in order not to make enemies.
"I decided not to keep quiet this time to ensure that episodes like this do not happen again," he said, adding that such behaviour would be "seriously condemned outside of Italy".
There have been numerous incidents of Black athletes in Italy suffering racist abuse.
In soccer, Black players are routinely jeered by fans, while in October Paola Egonu, a Black volleyball player, announced she was taking a break from the Italy national team following comments questioning her nationality.
