Ms. White, who is stepping into the lead role of Nora Helmer, Henrik Ibsen’s famous heroine, earned her most recent Tony nomination for her performance as Tanya in “Airline Highway,” in 2015. Charles Isherwood, reviewing the play in The New York Times, called her performance “indelible.”

“Ms. White’s fearless, vanity-free performance shows both the character’s innate warmth and a sad awareness of the self-destructive impulses that have left Tanya without much hope of redemption,” he wrote.

Stephen McKinley Henderson, a Tony nominee for the 2010 revival of “Fences,” will replace Mr. Cooper in the role of Torvald, the husband Nora leaves at the end of “A Doll’s House.” And Erin Wilhelmi, who made her Broadway debut in 2016 in a revival of “The Crucible” directed by Ivo Van Hove, will play Emmy, Ms. Rashad’s character.