A philanthropist who quit the board of the Cooper Hewitt, Smithsonian Design Museum to protest the termination of its director said on Thursday that she was also rescinding her $5 million bequest to the Upper East Side institution.

Judy Francis Zankel, who resigned as secretary of the board after Caroline Baumann was forced out by the Smithsonian, sent an email to Lonnie G. Bunch III, the top official, notifying him that she was cutting the Cooper Hewitt out of her will.

“I find your treatment of Caroline Baumann to be unconscionable and disgraceful,” Ms. Zankel said in her email to Mr. Bunch, in which she copied the rest of the Cooper Hewitt board. She called the investigation that led to Ms. Baumann’s ouster “biased” and said that she had also changed her mind about leaving the museum her collection of decorative objects.

“Although I love the museum and its work, I can no longer support an institution that functions this way,” she wrote.