West Hollywood- The Body Shop, a landmark strip club famed for giving Sunset Boulevard nude dancing and hundreds of struggling actresses work, was shuttered Wednesday after a dawn fire burned through its roof.

A cleaning crew discovered smoke billowing from a side door of the West Hollywood building when they arrived at 6:45 a.m.

No one was inside when the blaze began in the attic, the owner said. The kitchen, dressing room and office were seriously damaged.

In a 50-minute battle to extinguish the flames, two firefighters suffered minor injuries, said Los Angeles County Fire Inspector Frank Garrido.

The source of the fire seemed to be faulty electric wiring, said owner Salas Almudarris. He said he hoped to reopen the Body Shop in a month.

No damage estimate was available.

One of the Sunset Strip’s most venerable establishments, it opened in the 1940s as a burlesque club, Almudarris said.

He said his family bought the building in 1972, soon after the club had traded in relatively tame revues — a topless woman swimming in an oversized champagne glass — for all-nude dancing.

A former dancer, Nancy Deedrick, said she performed the Strip’s first completely naked dance at the Body Shop in the 1970s.

At the time, she said, it was such a big deal that Johnny Carson invited her on his television show. She turned him down for fear of embarrassing her family, she said.

“Every famous stripper in the world has worked there,” said Deedrick, now retired and living in Tennessee.

The club has remained popular with Hollywood, Almudarris said. Motley Crue named the club as one of its favorite strip joints in the 1987 hit “Girls, Girls, Girls.”

“We got princes, actors, comedians,” Almudarris said. “Every movie star you could mention has been in here.”

Courtney Love was one of the many women trying to break into show business who worked at the Body Shop, he said.

“She came back to visit about four years ago,” Almudarris said. “She sat in the dressing room and talked to the girls.”

He said listing the others who spent their before-they-were-stars years on the club stage would invade their privacy. What about the rumor that Demi Moore trained at the Body Shop to prepare for her role in “Striptease”?

“She’s been here,” is all Almudarris would allow.

Standing outside the club on ground strewn with charred business records and water-logged chairs, he fielded questions from insurance representatives and comforted employees who stopped by, including some of the club’s about 50 dancers.

One women shook her head and accepted a hug from a male colleague.

“I’ve never actually seen you in daylight,” she told him.