Trump claimed that Winfrey posed "biased and slanted" questions to a panel on the CBS news program. He also added that he hoped she would run for office so "she can be exposed and defeated just like all the others."
Winfrey, a talk show host, actress and philanthropist, made her debut on "60 Minutes" as a correspondent in September last year with a story about the political divide in the U.S.
She accepted the Golden Globes' Cecil B. DeMille Award for lifetime achievement last month, and gave an acceptance speech that explored issues of race, gender and other social and political hot buttons.
Her speech gave rise to speculation of a potential presidential bid in 2020, but Winfrey has denied any such plans.