Israel's prison service denied the allegations, and Reuters was not able to verify them independently.
Germany's foreign ministry said some of the country's citizens had been injured and that some accusations were "serious".
A legal source in Italy said prosecutors there were investigating possible crimes including kidnapping and sexual assault.
"The allegations raised are false and entirely without factual basis," an Israeli prison service spokesperson said in a statement.
"All prisoners and detainees are held in accordance with the law, with full regard for their basic rights and under the supervision of professional and trained prison staff," it said.
"Medical care is provided according to professional medical judgment and in accordance with Ministry of Health guidelines."
The Israeli military referred queries to the foreign ministry, which referred them to the prison service.
Israeli forces arrested 430 people on board 50 ships in international waters on Tuesday to halt a flotilla of volunteers trying to bring aid supplies to the Gaza Strip.
The allegations of abuse will add to pressure on Israeli authorities to explain the treatment of the detainees, after video of an Israeli cabinet minister in a prison mocking some of the activists sparked an international outcry.
"We're very concerned by these reports," United Nations spokesman Stephane Dujarric said when asked about the allegations at a regular briefing on Friday.
Global Sumud Flotilla, the organisers of the aid shipment, said the group had documented at least 15 cases of sexual abuse, with the worst occurring on one Israeli landing craft which had been converted into a makeshift prison with barbed wire and shipping containers.
Detainees were thrown into the containers and beaten over the head and ribs, the group said in a statement.
They suffered multiple cases of sexual abuse, including "humiliating strip searches, sexual taunting, groping and pulling of genitals, and multiple accounts of rape".
"At least 12 sexual assaults have been documented on that vessel alone, including anal rape and forcible penetration by a handgun," it added.
The statement was released after the Israeli prison service's blanket denial of mistreatment, rape and sexual assault allegations.
Reuters sent the additional specific allegations to the prison service but did not receive a reply after hours on Friday, a holiday in Israel.
Mi Hoa Lee, an activist from Spain, said she was forced into the darkened container on the ship, according to a video interview included with the flotilla's statement.
"Four men started beating me in the face against the wall, and I fell down and then stood up again, again to the floor, stood up again, and they started tasering me for more than one minute," she said, pointing to her ribcage, hips and back where she said they applied the taser.
"Then they kept beating me until I almost lost my conscience," she added.
Ilaria Mancosu, an Italian activist, told Reuters the flotilla members were removed from their boats to two so-called prison ships.
Those put on one of the ships suffered more violence than the other, she said.
They were locked in a container and beaten by five soldiers, suffering fractures to the ribs and arms.
Some had serious injuries to their eyes and ears caused by tasers.
She said they spent two days on the prison ships with no running water and used cardboard and plastic to keep warm at night, since they had no blankets and were stripped of most of their clothes.
Once on land they were made to kneel for several hours and kicked and shoved if they moved or spoke.
They were then taken to a prison where they were moved from room to room periodically to keep them from sleeping, she said.
