The Blues have released a statement following a media report and widespread speculation, which focused on an apparent party at a Carlton player's house on Saturday night.
The Seven Network reported multiple players from Carlton required hospitalisation after alleged recreational drug use.
AAP is not suggesting recreational drugs were involved in Hayward or Cowan's hospital visits.
Ambulance Victoria confirmed to AAP that advanced life support paramedics responded to an incident at inner-suburban South Yarra at around 5.15am on Sunday.
They added a man in his 20s was taken by ambulance to The Alfred Hospital in stable condition.
The Blues also issued their statement, naming Hayward, 27, and Cowan, 21, while providing more details around their mishaps.
"Carlton can confirm that Lachie Cowan and Will Hayward were admitted to hospital under separate circumstances on Sunday morning," the club wrote.
"Cowan received medical treatment and underwent observation, before being discharged a short time later.
"Will Hayward experienced a minor cut to the head after a fall, and admitted himself to hospital where he received stitches before being discharged.
"The club has been in regular contact with both players, with priority for their wellbeing and both players have now received the necessary care relating to their separate circumstances."
The AFL have been contacted by AAP for comment.
Players throughout the league are currently on leave as trade period rolls on until Wednesday night.
The AFL revealed its new illicit drugs policy in March this year, with chief executive Andrew Dillon trumpeting it as "the most stringent illicit drugs policy in Australian sport".
"The reality is illicit drug use is not an issue unique to sport - it is a broader societal challenge, and our players are not immune from the issues and pressures that exist in the community," Dillon said at the time.
"This revised policy is stronger, more comprehensive and more rigorous. It combines mandatory education, universal hair testing, treatment, monitoring and ongoing support across both AFL and AFLW."
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