David Sweat, 35, was shot twice in the torso by a state trooper just south of the Canadian border on Sunday.
He was transported to a hospital in the state capital Albany, where he was initially listed in critical condition.
Albany Medical Center medical director Dennis McKenna said doctors evaluated Sweat and determined he did not need surgery.
"His condition has been upgraded to serious, reflecting an improvement from his condition Sunday night," McKenna said in a statement.
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The manhunt's dramatic conclusion came when a state trooper spotted Sweat on a road less than two miles south of the Canadian border.
The fugitive made a dash for a line of trees and refused commands to stop, according to New York Governor Andrew Cuomo. The trooper then shot Sweat, fearing he would disappear into the trees.
Sweat had escaped from the Clinton Correctional Facility in upstate New York along with fellow inmate Richard Matt on June 6.
Matt was shot dead by a federal agent on Friday.