The Oilers, through Cave's family, provided an update on Cave's status Thursday on their Twitter account.
"This is giving his brain time to heal & rest from all he's been through," the team wrote in the post.
The 25-year-old native of Battleford, Saskatchewan, was airlifted Tuesday to Sunnybrook Hospital and underwent emergency surgery. Doctors removed a colloid cyst that was causing pressure on his brain.
"It's devastating, but Colby is one of the toughest guys I know," Oilers captain Connor McDavid said, according to the team. "If anyone is going to get through this, it's him. We're right there with him in the fight."
Cave's wife, Emily, posted an update on Instagram on Wednesday after seeing him through a window with his parents and talking to him via a walkie-talkie.
"My heart is shattered into a million pieces without my best friend," she wrote.
View this post on Instagram
Please wake up. Please wake up. It's all I can keep asking, "he's going to wake up right?" We need a miracle. Colby's parents and myself, got to see him through a window and talk to him with a walkie talkie last night. We are no longer allowed to be in the hospital because Covid-19 rules. We have no idea when we will be allowed to see him again. The nurse has tied his wedding band to his ankle. I am dreaming of being able to touch you, hear your voice, squeeze your hand (3 times), and kiss you again. I love you so much, and my heart is shattered into a million pieces without my best friend 💛✨ Out of difficulties grows miracles- 1 Peter 5:10
Emily Cave said the family is no longer allowed to be in the hospital because of COVID-19 rules. She said they have no idea when they will be allowed to see him again.
Cave scored one goal in 11 games with Edmonton this season. He has four goals and five assists over 67 NHL games with Boston and Edmonton.
The Associated Press contributed to this report.