Ramadan, a Swiss national who is now a leading Oxford professor, vowed legal action over claims reported by the Tribune de Geneve newspaper on Saturday.
"Anonymous allegations have been made against me in Geneva accusing me of the abuse of students who were minors nearly 25 years ago," Ramadan said on Twitter.
"I categorically deny these allegations," he said, adding that he was filing a libel suit.
Ramadan, 55, is also facing investigations in France for the alleged rape of two women, which he denies.
The Tribune de Geneve said it spoke to four women who had been Ramadan's students in the 1980s and 1990s, when he taught at public schools in Geneva.
One woman, identified as Lea, said she was forced to fend off his sexual advances when she was 14.
Three others, whose ages ranged from 15 to 18 at the time, told the paper that Ramadan used his authority as their teacher to initiate sexual relationships.
Geneva justice ministry spokesman Henri Della Casa told AFP that he had no information regarding any criminal complaints made against Ramadan, whose grandfather founded Egypt's Muslim Brotherhood Islamist movement.
Della Casa did not immediately respond when asked if Ramadan had yet filed a libel case in Swiss courts.
Geneva education officials were also quoted in local media as saying that they received no allegations of misconduct against Ramadan while he was teaching in the city.
Ramadan has filed counter-charges for libel regarding the French allegations, which he has denounced as a "campaign of lies launched by my adversaries".
Henda Ayari lodged a rape complaint against Ramadan over an alleged 2012 assault in a Paris hotel.
A second, unidentified woman accused him of raping her in a hotel room in 2009.
Ramadan, a professor of contemporary Islamic studies at Oxford University, is popular among conservative Muslims, while secular critics accuse him of promoting a political form of Islam.
The claims against him followed a surge in public discussion about sexual assault triggered by the multiple allegations against Hollywood mogul Harvey Weinstein.