On Twitter on Thursday, his post said: “A “not no great” ICU DAY, turned to amazing spa day with my sis and mama. Thank you sooooo much.”
One of his family members is seen in the clip massaging his head.
The Avengers star has received well-wishes from fellow Marvel co-stars including Chris Hemsworth, Chris Evans, Chris Pratt and Paul Bettany as he recovers.
Other famous faces sending positive messages included Jimmy Fallon, Vanessa Hudgens, Penelope Cruz, Orlando Bloom and Heidi Klum.
He was airlifted to hospital on Sunday after suffering “blunt chest trauma and orthopaedic injuries” in an accident, a statement provided to the PA news agency, from his publicist, said.
The incident took place near the Mount Rose Highway, which links Lake Tahoe and south Reno, straddling the Nevada-California border.
At a press conference on Tuesday, Washoe County Sheriff Darin Balaam said Renner was helping a family member, who had become stuck in heavy snow, when the incident occurred.
Sheriff Balaam said: “Mr Renner went to retrieve his… SnowCat, an extremely large piece of snow removal equipment, weighing at least 14,330 pounds (6.4 tonnes), in an effort to get his vehicle moving.”
Renner also shared an update on his condition on Instagram that same day, posting a picture from his hospital bed with a bruised face.
In the post, Renner told fans he was “too messed up” to send a longer message.
“Thank you all for your kind words. I’m too messed up now to type. But I send love to you all,” he wrote.