The project, a partnership with the EarthCam webcam network, went live Monday at midnight.
Museum director Eric Shiner said the project is titled "Figment" because of a Warhol quote in which the artist said: "I always thought I'd like my own tombstone to be blank. No epitaph and no name. Well, actually, I'd like it to say, 'Figment.'"
The gravestone in a Pittsburgh suburb has Warhol's name, the dates of his birth and death and a cross. Warhol's 85th birthday would have been Tuesday.
Shortly after dawn Tuesday, the live video showed a star-shaped silver balloon and two smaller black-and-white balloons swaying gently in the breeze, next to a headstone surrounded by flowers and some decorative grasses.
Shiner said the museum, which is based in Pittsburgh, Warhol's hometown, decided that the gravesite webcam "would be a really fantastic way to put Andy on the air 24/7 and plug in to our global audience."
"We believe that this will give Warhol the pleasure of knowing that he is still plugged in and turned on over 25 years after his death," Shiner said.
Warhol, who died in 1987, was a devout Catholic who went to church every day to pray, Shiner said. He's buried near his parents at the St. John the Baptist Byzantine Catholic Cemetery in Bethel Park.
The Warhol gravesite also is documented in artist Madelyn Roehrig's ongoing art project "Figments: Conversations with Andy." Roehrig videotapes people who visit the grave and photographs the many objects adoring fans leave there.
Hundreds of people visit Warhol's grave every year, often leaving pop culture items featured in his artworks, such as Campbell's Soup cans and Coca-Cola bottles.
EarthCam said it also will have a live webcam from the church where Warhol was baptized and people will be able to send flowers and watch as they are delivered to the grave.