The country music star died aged 80 at a Nashville hospital following a "brief" battle with cancer, her representatives announced on Tuesday.
Parton starred alongside Jane Fonda and Lily Tomlin in the 1980 film 9 To 5 and later provided the music and lyrics for the stage adaptation.
Karla Tracey, who plays Parton's character Doralee, broke the news to the audience at the Pavilion Theatre in Worthing, West Sussex, before paying tribute to the singer.
"Tonight, we will perform the piece as she intended with great respect and affection for the woman whose vision brought it to life," Tracey said.
"As we begin, we dedicate tonight's performance to Dolly Parton, with our deepest thanks for the music, laughter and joy she gave us."
The singer was best known for her genre-defining hits including 9 To 5, I Will Always Love You and Jolene.
Paul Jepson, Landmark Theatres chief executive and the musical's director, said: "We would like to take a moment to remember the remarkable Dolly Parton.
"Our thoughts are with Dolly's family, friends and all those around the world who loved and admired her.
"It has been an honour for all of us to work on this show, originally written and produced by Dolly, whose extraordinary talent, creativity and spirit are woven into every part."
A musical about Parton's life, Dolly: A True Original Musical, is due to begin previews on Broadway later in 2026 before opening night in January 2027, on what would have been Parton's 81st birthday.
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