The 58-year-old double Oscar winner, who plays ruthless President Francis Underwood in the hit show, is facing claims from Star Trek: Discovery actor Anthony Rapp that he "made a sexual advance" at a party 31 years ago while Rapp was underage.
"Season six is our last season," a spokeswoman told AFP.
Starring alongside Robin Wright, Spacey is also executive producer of the platform's flagship series, which is adapted from a BBC drama of the same name and has earned 46 Emmy nominations and Golden Globes for its lead couple.
Netflix doesn't release viewing figures. But the show has marked out its place in television history as the company's debut in original programming, which has grown to include other highly regarded shows such as Stranger Things and Orange Is the New Black.
Filming for season six is under way in Maryland, with season six expected to drop next year. No premiere date has yet been set but House of Cards has never debuted later than May.
Rapp, 46, told Buzzfeed that in 1986, while both he and Spacey were performing on Broadway, Spacey invited the then 14-year-old to a party at his New York home. Spacey would have been 26 at the time.
Rapp said he was in Spacey's bedroom watching TV when Spacey, apparently drunk, came in after all the other guests had left, and lay on top of him.
"He was trying to seduce me," Rapp told Buzzfeed. "I don't know if I would have used that language. But I was aware that he was trying to get with me sexually."
Spacey apologised on Twitter, and went on to say that Rapp's accusation "encouraged me to address other things about my life" before confirming that he was gay.
His comments prompted a backlash from critics who accused him of deflecting from his misdeed by finally coming out, while reports suggested that he may face other accusers.
Netflix and House of Cards production company Media Rights Capital issued a joint statement saying they were "deeply troubled" the allegations against Spacey, who is currently not scheduled to be on set.
"In response to last night's revelations, executives from both of our companies arrived in Baltimore this afternoon to meet with our cast and crew to ensure that they continue to feel safe and supported," it said.