Reeve fell into a coma on Saturday after going into cardiac arrest while at his New York home and died on Sunday, his publicist said.
Reeve was being treated at Northern Westchester Hospital for a pressure wound that he developed, a common complication for people living with paralysis.
In the past week, the wound had become severely infected, resulting in a serious systemic infection.
"On behalf of my entire family, I want to thank Northern Westchester Hospital for the excellent care they provided to my husband," Dana Reeve, Christopher's wife, said in a statement.
"I also want to thank his personal staff of nurses and aides, as well as the millions of fans from around the world who have supported and loved my husband over the years."
Reeve had a near-fatal riding accident nine years ago which turned him into a worldwide advocate for spinal cord research.
Reeve broke his neck in May 1995 when he was thrown from his horse during an equestrian competition in Culpeper, Virginia.
Enduring months of therapy to allow him to breathe for longer and longer periods without a respirator, Reeve emerged to lobby Congress for better insurance protection against catastrophic injury and to move an Academy Award audience to tears with a call for more films about social issues.
In 2000, Reeve was able to move his index finger, and a specialised workout regime made his legs and arms stronger. He had also regained sensation in other parts of his body.
He leaves behind his wife, two sons and a daughter.