A convicted murderer who escaped from a maximum-security New York prison three weeks ago has been shot and captured, authorities and media say, two days after his fellow escapee was shot dead.

David Sweat was wounded just 3km south of the Canadian border and taken to hospital, several television networks reported, citing unnamed law enforcement sources.

The Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) confirmed on Twitter that Sweat had been captured.

"Sleep peacefully New York," the federal agency wrote, without providing additional details.

Sweat's shooting brings to a head a spectacular, weeks-long manhunt that saw hundreds of law enforcement officers working around the clock to scour the rugged, remote area around the Clinton Correctional Facility in upstate New York after the inmates busted out on June 6.

Sweat, 35, and Richard Matt, 49, had escaped in an audacious act in which they used power tools to cut through cell walls, then crawled through pipes to emerge from a manhole in the village of Dannemora, home to the sprawling prison.

Two prison workers have been charged over the brazen breakout, and are accused of smuggling tools and contraband items to the pair in hamburger meat.

The escape triggered an intense manhunt involving about 1300 personnel backed by sniffer dogs and helicopters.

Matt was killed on Friday in the town of Malone, less than 16km from the Canadian border, after he apparently fired at a passing camper van.

An autopsy found that he died from three bullet wounds to the head after a US Customs and Border Protection agent opened fire with a semi-automatic weapon.

CNN spoke to a small crowd that gathered outside the hospital where Sweat was being treated. Several residents expressed their relief that the lengthy manhunt had come to an end.

Sweat was serving a life sentence without parole for murdering a sheriff's deputy in New York state in 2002 when he was 22.

Matt was serving a sentence of 25 years to life for the 1997 kidnapping and dismembering of his former boss in a 27-hour ordeal.

He fled to Mexico after the murder and killed another American there, before being sentenced to 20 years and extradited back to New York.