"Colby is still in a medically induced coma. This is giving his brain time to heal and rest from all he's been through," the statement reads. "We would like to thank the Oilers organization, the entire hockey community, all of our friends, and family, and everyone who has shown us love and support.
"We would like to send a big thank you to Colby's critical care team, neurosurgeons, and nurses at Sunnybrook Hospital. We appreciate all that you are doing for our Colby."
Cave was admitted to hospital Monday after complaining about headaches and was later airlifted to Sunnybrook, where he entered intensive care.
His wife, Emily, took to Instagram on Wednesday night to also provide an update.
"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," she wrote. "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 (three times), and kiss you again. I love you so much, and my heart is shattered into a million pieces without my best friend."
Cave primarily spent his 2019-20 campaign with the Oilers' AHL affiliate in Bakersfield. The 25-year-old was with the Boston Bruins' organization before joining Edmonton last season.