The League One club had been on a pre-season training camp in Cornwall when the alleged incident took place, in Redruth.
A Devon and Cornwall Police spokesman confirmed the arrests. He said: "At 4.30am [today], police in Redruth received a complaint of sexual assault against a woman aged in her early 20s.
"The incident is alleged to have occurred at a property in Redruth. As a result of inquiries, five men aged 35, 19, 18 and two aged 24 were arrested in connection with the incident. They remain in custody centres in Camborne and Newquay.
"Earlier this evening, a sixth man was arrested in Cheshire, aged 21 years. He will be taken back to Cornwall where he will be formally interviewed."
A spokesman for the club tonight confirmed Crewe players were being held.
He said: "I can confirm some players have been arrested.
"From what we know there are three arrested and two helping with inquiries over an alleged sexual assault.
"The details are a bit sketchy so we can't really comment at the moment."