The 30-year-old was being held for questioning by Cleveland Police following an incident in the early hours.
A force spokeswoman said: "A 30-year-old man from Wynyard has been arrested on suspicion of sexual assault and possession of a class A drug.
"He is currently being questioned by police and inquiries are ongoing."
The club said it was making inquiries but did not want to say anything more at this time.
A Sunderland spokesman said: "The club is looking into this matter but due to ongoing police investigations is unable to comment further at this stage."
Bramble's career started at his hometown club, Ipswich, before he moved to Newcastle under Sir Bobby Robson for £6million in 2002.
After five years on Tyneside he joined Wigan before returning to the north east with Sunderland last year.
The powerful but sometimes error-prone centre-back played 10 times for England Under-21s.