In "Tales of the Plague", his adaptation of the Medieval Italian series "The Decameron", the 78-year-old Vargas plays Duke Ugolino, a 14th century nobleman.
The author has appeared in recitations of his earlier work but this is his first fully acted stage role, which he has called it a "terrifying" experience.
"I'm nervous, very nervous. I feel terror, panic, fear," he told reporters.
"At the same time it is so stimulating and exciting. It is such a novel and rejuvenating experience."
He said his play was inspired by 14th century Italian writer Giovanni Boccaccio's prose masterpiece, but much shorter. The original contains 100 tales but the Madrid show lasts less than two hours.
The auditorium of Madrid's old opera house the Teatro Real has also been adapted, so the play can be performed in the round. It runs from January 28th to March 1st.
In the play, the duke and four other characters tell stories as they hide away to try and escape a plague in 14th century Florence.
Vargas Llosa is best known in the English-speaking world for novels such as "The Time of the Hero" and "The War of the End of the World".
He received the Nobel Prize for Literature in 2010.
A journalist and prominent public intellectual as well as a novelist and playwright, he drew a topical parallel with the plague tale.
"Terrorism is a plague of our times," he said, while culture "is an extraordinary weapon we have to defend ourselves in adversity".