The ex-BBC radio DJ follows Gary Glitter and Freddie Starr as the third celebrity to be questioned by police investigating allegations made against late star Jimmy Savile.
Travis was arrested at his Bedfordshire home at 7.45am as part of the Metropolitan Police investigation Operation Yewtree.
The police, who did not confirm Travis's name, said that the arrest "falls under the strand of the investigation we have termed 'Others'", which means it is not directly related to abuse by Savile.
In the spate of allegations made in the wake of Savile's abuse being exposed, ex-Sky presenter Vivien Creegor, 55, claimed that Travis had molested her breasts during a Radio 4 broadcast, while another woman claimed he had put his hand up her skirt.
Travis told The Sun at the time: "It's nonsense, completely untrue.
"If police get in touch, I'm happy to get it sorted. I hate being tarred with the same brush as Savile."
Officers now say that 200 allegations of sexual assault have been made while 450 potential victims have come forward.
A fourth man, ex-BBC producer Wilfred De'Ath, was arrested on suspicion of sexual offences as part of Operation Yewtree on Sunday (November 11) and bailed until December.