A NASA spokesman talked to Armstrong's wife, Carol, on Wednesday and said only that he was recovering. Armstrong's birthday was Sunday.
It wasn't clear where the surgery occurred or where the former astronaut was recuperating.
NASA Administrator Charles Bolden wished Armstrong a quick recovery from cardiac bypass surgery in a Facebook statement.
"Neil's pioneering spirit will surely serve him well in this challenging time and the entire NASA Family is holding the Armstrong family in our thoughts and prayers," the statement said.
Armstrong commanded the Apollo 11 spacecraft that landed on the moon on July 20, 1969, and he radioed back to Earth the historic news of "one giant leap for mankind." He spent nearly three hours walking on the moon with fellow astronaut Edwin "Buzz" Aldrin.
A message Wednesday on Aldrin's Twitter account also wished Armstrong well. Armstrong and his wife married in 1999 and made their home in the Cincinnati suburb of Indian Hill, but he has largely stayed out of public view in recent years.
He spoke at Ohio State University during a February event honoring fellow astronaut John Glenn and the 50th anniversary of Glenn becoming the first American to orbit the Earth. In May, Armstrong joined Gene Cernan, the last man to walk on the moon, at Pensacola Naval Air Station in Florida to support the opening of The National Flight Academy, which aims to teach math and science to kids through an aviation-oriented camp.