"Thank you renowned medical ICU team for beginning this journey," Renner wrote on an image shared to his Instagram story.
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The snapshot shows the actor in a hospital bed, surrounded by medical professionals.
The late Friday post is the third update Renner shared since being hospitalized. He underwent two surgeries for blunt chest trauma and orthopedic injuries after he was crushed by a snowplow on New Year's Day near his Nevada home.
The Marvel star was clearing snow from a private driveway when the accident occurred, his publicist previously told CNN.
Renner also shared a brief video of supporters dancing to 50 Cent's "In Da Club" to wish him a happy birthday, and he thanked them for the "birthday love."
Several other actors also sent birthday wishes to Renner. "Happy birthday to one of the toughest guys I know," wrote Chris Evans on his Instagram story with a picture of Renner. "Sending so much love your way."
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Washoe County Sheriff Darin Balaam said at a Tuesday news conference that Renner's snowcat, an engine-powered machine used to clear snow, started to roll away while Renner was not in the driver's seat.
He was injured as he tried to get back into the machine, Balaam said. Renner's family members were with him when he was injured.
Authorities received a 911 call about the accident on New Year's morning. The highway was closed due to severe winter weather. Because of the difficult weather, a helicopter was used to transport Renner to the hospital.
CNN contributed to this story.