Concerns were reportedly raised over the pilots before the 9am United Airlines UA162 flight to Newark, New Jersey, was due to depart from Glasgow Airport on Saturday.
Police said the two men - aged 35 and 45 - were arrested and detained in police custody.
The flight, carrying 141 passengers, eventually took off on Saturday evening with a new crew on board.
The men are expected to appear at Paisley Sheriff Court on Monday.
A Police Scotland spokesman said: “Police Scotland can confirm that two men aged 35 and 45 have been arrested and are presently detained in police custody in connection with alleged offences under the Railways and Transport Safety Act 2003, Section 93.”
The section of the Act relates to carrying out pilot function or activity while exceeding the prescribed limit of alcohol.
A spokesman for Glasgow Airport added: “We are aware of the police incident yesterday involving two pilots.”
The incident follows the appearance in court last month of two Canadian pilots charged with being drunk as they prepared to fly a passenger jet from Scotland to Toronto.
Jean-Francois Perreault, 39, and Imran Zafar Syed, 37, were arrested on Monday July 18 before they were due to take off on the Air Transat flight from Glasgow Airport.
The men were remanded in custody when they first appeared at Paisley Sheriff Court, also charged under section 93 of the same Act.
At a second hearing at the same court they were granted bail on condition they surrender their passports.
Section 93 of the Railway and Transport Safety Act states: ‘’A person commits an offence if he performs an aviation function at a time when the proportion of alcohol in his breath, blood or urine exceeds the prescribed limit, or he carries out an activity which is ancillary to an aviation function at a time when the proportion of alcohol in his breath, blood or urine exceeds the prescribed limit.’’
For pilots, the limit of alcohol in the case of breath is nine microgrammes of alcohol in 100 millilitres, according to the Act.
A spokesman for United Airlines said: “The two pilots have been removed from service and their flying duties.
“We are co-operating with the authorities and will conduct our own investigation as well. The safety of our customers and crew is our highest priority.”