Davis was said to be shocked at the news of Vidal's sudden death this week at his home in LA. He had suffered from complications following pneumonia.
She will dedicate an extra special performance to the Best Man playwright on Wednesday (August 8). The Sex and the City star took to Twitter to pay her respects.
She wrote: "Rest in peace our brilliant writer - so sad to loose (sic) him. We will relish his words today in TheBestManBway."
Other stars also tweeted about the literary great. Whoopi Goldberg wrote: "Gore Vidal 1 of the smartest, wittiest minds has left us. Read him if you haven't see his play... (sic)."
The Best Man had its Broadway debut back in 1960 and was nominated for countless Tony awards. It is currently wowing audiences in New York.
The cast includes Davis, James Earl Jones, Cybill Shepherd and John Stamos.