"It is unseemly to undress on stage. I won't do that," she said.
Collins, 67, best known for her role as scheming Alexis in TV series Dynasty, told the Sunday Express she had flatly refused to take the part of the middle-aged temptress.
"It is unseemly to undress on stage. I won't do that," she said.
Hollywood star Kathleen Turner is currently playing Mrs Robinson, immortalised by Anne Bancroft in the 1967 film, and the Simon and Garfunkel song of the same name.
In a memorable part of the play, Turner drops her towel to bare all for a few seconds. But in the film the famous seduction scene saw Bancroft tantalise Dustin Hoffman with just a flash of stocking-clad leg.
'Just get on with it'
Turner, star of films such as Body Heat and Romancing the Stone, said: "Of course you get nervous about the nudity but its just another part of being an actress.
"If the role demands it, and with Mrs Robinson I think it definitely does, then you just get on with it."
Collins, who bared all for Playboy at age 50, is said to be keen to perform in the West End after a successful American theatrical run in Love Letters.
However her publicist Stella Wilson said: "Joan was offered the part but didn't want to do it because she didn't want to take her clothes off."
Texan model Jerry Hall is currently rehearsing to take over the role from Turner on 31 July.
Hall is, it seems, just as unabashed about showing her body. In 1996, she stripped from the waist to pose for pictures by photographer David Bailey.
The almost nude photo was the first in her 25-year modelling career.
She told reporters then: "The strange thing is that when I was younger I was more insecure about my body than I am now."