"Adonis is now in a critical condition in intensive care at the hospital", Yvon Michel, Stevenson's promoter revealed via social media.
Stevenson lost his WBC and lineal light heavyweight titles when he was stopped by Gvozdyk in the 11th round of their bout.
The 41-year-old - nicknamed Superman - was stretchered out of the arena to a waiting ambulance.
The Montreal-based fighter was making his 10th title defence since winning the belt against Chad Dawson in 2013, and was ahead on points when he was stopped.
Gvozdyk (16-0, 13 KOs) landed eight unanswered punches, including a left hand and two crushing rights that badly hurt Stevenson (29-2-1, 24 KOs), who went down and slumped against one of the corner posts.
He made several attacks that failed to K-O Ukrainian Gvozdyk who, from the 7th round, began to be offensive against the native of Port-au-Prince.
At around 11:15 a.m., Michel tweeted on behalf of Stevenson's family and partner to thank the people who reached out with messages of encouragement and support.
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He was very confused when he arrived, we suspect a concussion. A few hours after the fight, Stevenson's promoter Yvon Michel released a statement on Twitter saying that Stevenson was in critical condition.
Stevenson fell early, in the third round, after getting hit by Gvozdyk.
Stevenson was taken to Quebec's Hôpital de l'Enfant-Jésus, which specializes in neurosurgery and head trauma. "This is very worrying".
He was down 96-94 and 98-92 at the time of the stoppage, but overcame horrific scoring to leave Canada as the new light heavyweight champion.
The boxing community took to social media to express their sympathies for a great champion of the sport.