The former Sex Pistol and Miss Spungen were staying in a room at the Chelsea Hotel in Manhattan.
Staff said Mr Vicious phoned room service to raise the alarm and then ran downstairs saying "something's happened to my girl".
Police called to the scene handcuffed Mr Vicious. As he was led away he shouted at a small crowd gathered to "sod off".
A New York police department spokesman says he will face a murder charge under his real name, John Ritchie. If proven guilty he could face life imprisonment.
The controversial punk rock star met Miss Spungen in London last year and moved to New York to work on a career outside of the Sex Pistols.
The band effectively split in January after lead singer Johnny Rotten walked out at the end of their US tour.
Police say Miss Spungen was found in Room 100 dressed only in her underwear with stab wounds to her stomach. They also retrieved "drugs paraphernalia".
The pair were in the spotlight earlier this year after being charged in London for possession of amphetamine. Friends say recently they had been visiting heroin addiction clinics.
Malcolm McLaren, Sid Vicious' manager, is expected to fly out to New York on the first plane tomorrow.
He said: "I can't believe he was involved in such a thing. Sid was set to marry Nancy in New York. He was very close to her and had quite a passionate affair with her."
But the former bass player's mother, Anne Beverley was critical of her son's relationship with Miss Spungen:
"I didn't like his girl. I called her Nauseating Nancy. She was a bad influence on my Sid."
Sid Vicious was widely regarded as becoming a Sex Pistols member more for his behaviour than his musical ability.
Sid Vicious' violent stage acts, self-mutilation and scorn for convention shocked the Establishment but made him the punk world's hero.
Sid pleaded not guilty to murder and was bailed for £50,000. He overdosed on heroin and died before any trial in February 1979. He was 21.
Both Nancy and Sid had unhappy backgrounds. Nancy was a heroin addict by the age of 15 and diagnosed schizophrenic. Sid was a disaffected school dropout.
Nils Stevenson, the Sex Pistols' tour manager once said that in time, Sid came to "dislike everything - except heroin and Nancy."