Mackay-Steven was pulled from the River Kelvin in Glasgow by firefighters.
The 26-year-old was on the bench for Aberdeen's 4-3 victory over Partick Thistle on Saturday and is believed to have been at a nearby nightclub with a fellow player on Saturday before the river rescue.
He was treated for hypothermia but is recovering well at home.
An Aberdeen spokesman said: "The club can confirm Gary Mackay-Steven was involved in an incident in the River Kelvin on Sunday morning.
"He was treated for hypothermia but is now at home and recovering well.
"On behalf of Gary, the club extends its thanks to the emergency services involved.
"The club will not be commenting further on the matter."
Firefighters were called to reports of a man in the water at the River Kelvin near Benalder Bridge in Glasgow at 2.46am on Sunday August 27.
A Scottish Fire and Rescue Service spokesman said: "Four appliances attended and specialist water rescue crews safely assisted the individual out of the water - he was then transferred into the care of paramedics after suffering the effects of hypothermia.
"Firefighters ensured the area was safe before leaving the scene."
Police Scotland said the casualty was taken to Queen Elizabeth University Hospital for treatment.
A force spokeswoman said: "Around 2.40am on Sunday, August 27, police received a report of a 26-year-old male in the River Kelvin, Partick.
"Emergency services attended and a full search of the area was carried out with the male being located.
"He was taken to the Queen Elizabeth University Hospital."
Source: Daily Express