The veteran comedian, 73, was questioned by North Yorkshire Police on 26 April in relation to the incident, which is reported to have taken place in Harrogate.
The TV personality’s name had not been revealed until the Daily Mail named him on Monday night.
It is understood that Mr Tarbuck was arrested at his home in Kingston upon Thames, London. The arrest followed Metropolitan Police officers, working on the Jimmy Savile sex abuse investigation Operation Yewtree, passing information to North Yorkshire Police.
A spokesman for North Yorkshire Police said: “North Yorkshire Police can confirm that a 73-year-old man has been arrested in connection with a historic child sex abuse investigation in Harrogate.
“The man was arrested in Kingston Upon Thames on Friday 26 April 2013. Following questioning, he was released on police bail pending further inquiries.
“The complaint relates to an incident that occurred in the late 1970s when the victim was a young boy. It would not be appropriate to comment further at this stage.”
Mr Tarbuck has spent more than 50 years working in television, including hosting quiz shows such as Winner Takes All and Full Swing. In 1994 he was awarded an OBE by the Queen for services to showbusiness and charity.
His agent could not be contacted for comment on Monday evening.