Police were called to the Holiday Inn in Preston city centre in the early hours of Wednesday.
They had received reports that people were smoking a suspicious substance in the hotel bar.
Mr White's hotel room was raided and he was arrested after a white powder was recovered. He was questioned and released on bail until 21 April.
A Lancashire Police spokesman said the substance will now undergo forensic testing.
No one else was arrested in connection with the incident.
Mr White was unavailable for comment on Wednesday.
"A man has been released on bail in order for the substance to be tested," said the police spokesman.
Substance will be tested
A spokeswoman at the Holiday Inn at Ringway, Preston, refused to comment further on the arrest.
"We can confirm that an incident has taken place, but as it has been handed over to the police we do not wish to comment."
He was in Preston to play an exhibition match with Alex Higgins at the Guildhall.
Alan Baker, general manager at Preston's Guildhall, said around 1,000 people attended Tuesday night's match, which was part of a UK tour.
Mr White, who was beaten in the European Open Championships in Malta on 6 March, has not won a major title since 1992.
His first round match at this year's World Championships takes place on 19 and 20 April.