The 22-year-old midfielder, from Glasgow, was stopped by police for driving erratically in the Robroyston area at about 03:00 on 5 February.
Officers asked him to provide a breath test and he gave an alcohol reading of 78mg - the legal limit is 22.
Sheriff Neil Mackinnin disqualified the player for 12 months and also fined him £500. The sheriff allowed him to do a drink driving course which, if successfully completed, would reduce the ban.
Last August, McGregor was banned from driving for four months and fined £400 after being caught driving at 69mph in a 50mph zone.
McGregor began as a youth player at Celtic and spent a year on loan at English side Notts County in the 2013-14 season.
He returned to Celtic and scored in his first-team debut against KR Reykjavik in a Champions League qualifier in 2014.