The Tribune de Geneve newspaper quoted Geneva's prosecutor's office spokesman Henri Della Casa as saying that authorities had decided to open a formal criminal inquiry into allegations that Ramadan raped a woman in a Geneva hotel in 2008.
"I confirm the opening of an inquiry," the paper quoted Della Casa as saying, a key step that indicated the authorities believed the allegations merit further investigation.
The accuser lodged her complaint in April.
"The prosecutors and Geneva police have worked quickly and worked well," Romain Jordan, the lawyer representing Ramadan's Swiss accuser, told AFP in an email.
He described the decision to open a criminal inquiry as "a major advance" that "demonstrates the seriousness of the allegations made by our client."
Ramadan, a Swiss citizen whose grandfather founded Egypt's Muslim Brotherhood movement, has not yet been interviewed by Swiss prosecutors.
Jordan said that following the opening of a criminal case, Swiss investigators will now have to travel to France to hear Ramadan's side of the alleged rape.
The 56-year-old scholar, a prominent and controversial figure within Islam, has denied any criminal wrongdoing.
Ramadan, who took leave from his post at Oxford University after the allegations surfaced, has complained that his imprisonment has made it more difficult for him to receive treatment for multiple sclerosis.
Ramadan, a married father of four who is one of European Islam's best-known figures, is being held in a prison hospital in Fresnes, south of Paris.
On Tuesday, Ramadan will be questioned in the presence of a second accuser, a disabled woman identified as "Christelle" who claims he raped and beat her in a hotel in the southeastern French city of Lyon in 2009.