The officer responsible for investigating the death, Teerapop Luanseng, said the 72-year-old actor was staying at a suite at the luxury Swissotel Nai Lert Park Hotel.
"I can confirm that we found his body, naked, hanging in the closet," Teerapop said. He said police suspected suicide.
A spokesman for the U.S. Embassy, Michael Turner, said the embassy was informed by Thai authorities that Carradine died either late Wednesday or early Thursday, but he could not provide further details out of consideration for his family.
Chuck Binder, a member of Carradine's management team, told CBS News that Carradine was in Bangkok shooting a film.
Carradine came from an acting family. His father, John, made a career playing creepy, eccentric characters in film and on stage. His brothers Keith, Robert and Bruce also became actors. Actress Martha Plimpton is Keith Carradine's daughter.
"My Uncle David was a brilliantly talented, fiercely intelligent and generous man. He was the nexus of our family in so many ways, and drew us together over the years and kept us connected," Plimpton said Thursday.
Carradine was in Bangkok shooting the movie "Stretch," said his manager, Chuck Binder.
"We're very saddened, he was a wonderful guy," said Lori Binder, a partner in the agency that represented Carradine.
"It is shocking to me that he is no longer with us," said Michael Madsen, who played an assassin in "Kill Bill."
"I had been thinking about calling him for the last several days. ... I have so many great memories of David that I wouldn't even know where to begin. He has a very special place in my heart."
The Web site of the Thai newspaper The Nation said Carradine could not be contacted after he failed to appear for a meal with the rest of the film crew on Wednesday, and that his body was found by a hotel maid Thursday morning. It said a preliminary police investigation found that he had hanged himself with a cord used with the suite's curtains. It cited police as saying there was no sign that he had been assaulted.
Police said Carradine's body was taken to a hospital for an autopsy that would be done Friday.
Carradine appeared in more than 100 feature films with such directors as Martin Scorsese, Ingmar Bergman and Hal Ashby. One of his early film roles was as folk singer Woody Guthrie in Ashby's 1976 biopic, "Bound for Glory."
But he was best known for his role as Kwai Chang Caine, a Shaolin priest traveling the 1800s American frontier West in the TV series "Kung Fu," which aired in 1972-75.
"I wasn't like a TV star in those days, I was like a rock 'n' roll star," Carradine said in an interview with Associated Press Radio in 1996. "It was a phenomenon kind of thing. ... It was very special."
Actor Rainn Wilson, star of TV's "The Office," tweeted about Carradine's death on Twitter: "R.I.P. David Carradine. You were a true hero to so many of us children of the 70s. We'll miss you, Kwai Chang Caine."
Carradine reprised the role in a mid-1980s TV movie and played Caine's grandson in the 1990s syndicated series "Kung Fu: The Legend Continues."
He returned to the top in recent years as the title character in Quentin Tarantino's two-part saga "Kill Bill." Bill, the worldly father figure of a pack of crack assassins, was a shadowy presence in 2003's "Kill Bill - Vol. 1." In that film, one of Bill's former assassins (Uma Thurman) begins a vengeful rampage against her old associates, including Bill.
In "Kill Bill - Vol. 2," released in 2004, Thurman's character catches up to Bill. The role brought Carradine a Golden Globe nomination as best supporting actor.
Bill was a complete contrast to Caine, the soft-spoken refugee from a Shaolin monastery, serenely spreading wisdom and battling bad guys in the Old West. He left after three seasons, saying the show had started to repeat itself.
"David's always been kind of a seeker of knowledge and of wisdom in his own inimitable way," his brother, actor Keith Carradine, said in a 1995 interview.
After "Kung Fu," Carradine starred in the 1975 cult flick "Death Race 2000." He starred with Liv Ullmann in Bergman's "The Serpent's Egg" in 1977 and with his brothers in the 1980 Western "The Long Riders."
But after the early 1980s, he spent two decades doing mostly low-budget films. Tarantino's films changed that.
"All I've ever needed since I more or less retired from studio films a couple of decades ago ... is just to be in one," Carradine told The Associated Press in 2004.
"There isn't anything that Anthony Hopkins or Clint Eastwood or Sean Connery or any of those old guys are doing that I couldn't do," he said. "All that was ever required was somebody with Quentin's courage to take and put me in the spotlight."
One thing remained a constant after "Kung Fu": Carradine's interest in Asian herbs, exercise and philosophy. He wrote a personal memoir called "Spirit of Shaolin" and continued to make instructional videos on tai chi and other martial arts.
In the 2004 interview, Carradine talked candidly about his past boozing and narcotics use, but said he had put all that behind him and stuck to coffee and cigarettes.
"I didn't like the way I looked, for one thing. You're kind of out of control emotionally when you drink that much. I was quicker to anger."
"You're probably witnessing the last time I will ever answer those questions," Carradine said. "Because this is a regeneration. It is a renaissance. It is the start of a new career for me.
"It's time to do nothing but look forward."