Renner is currently starring in the Paramount+ series The Mayor of Kingstown.
A spokesperson for the actor told US entertainment outlet Deadline the 51-year-old was airlifted to hospital on Sunday after the incident, which occurred while he was ploughing snow.
The spokesperson added Renner was with his family and “receiving excellent care”.
"We can confirm Jeremy is in critical but stable condition with injuries suffered after experiencing a weather-related accident while ploughing snow earlier today,” a representative of Renner told Deadline.
It came as dozens of people were killed across the US amid blizzard conditions.
The Arctic blast stirred up heavy winds and snow, trapping some residents inside their houses with snowdrifts and knocking out power to tens of thousands of homes and businesses.
The scope of the storm has been nearly unprecedented, stretching from the Great Lakes near Canada down to the Rio Grande along the border with Mexico.
Renner previously tweeted about the snow at his US ranch in December, writing: “Lake Tahoe snowfall is no joke.”
The storm unleashed its full fury on Buffalo, with hurricane-force winds and snow causing whiteout conditions, in what has been branded one of the worst weather-related disasters to hit the western part of New York state.
Renner, a two-time Oscar nominee, is well-known for playing Hawkeye in the Marvel Cinematic Universe.
He has also featured in films including The Hurt Locker, American Hustle, and Mission Impossible – Ghost Protocol.
He is currently starring in Paramount+ series The Mayor Of Kingstown.