Police say John Ryan was tackled at Westchester Medical Center as he bolted through a door.
Two correction officers suffered minor injuries stopping the 59-year-old as he tried to escape Friday.
Ryan is on parole for a previous bank robbery and is charged with robbing a Bank of America in October in Callicoon, about 100 miles northwest of New York City.
Police say he threatened to detonate an explosive and made off with $80,000 before his getaway car was pulled over.
Ryan had been negotiating a deal to plead guilty and be released on bail before sentencing to be treated for the cancer. Authorities say he's a flight risk.