The couple's interracial marriage was the focus of at least three letters last week in which bodily harm was threatened, the New York Post (search) reported in Monday editions.
Diggs, who is black and stars in the UPN drama "Kevin Hill," and Menzel, who is white, were wed in January 2003.
Menzel arrived for the matinee performance in the company of five plainclothes guards, who remained stationed outside the stage door.
Menzel won a Tony award for her portrayal of Elphaba, the Wicked Witch of the West.
Diggs is currently filming in Canada.