The Equalities Minister accused the former Doctor Who star of being a "rich, lefty, white male celebrity so blinded by ideology" in a social media post yesterday.
Mr Tennant won Celebrity Ally at an LGBT awards ceremony on Friday for his support of the trans community.
He was cheered and applauded after saying he wished the Cabinet minister "doesn't exist", adding: "I don't wish ill of her, I just wish her to shut up."
The politician has spoken out about the Conservatives' pledge to change the 2010 Equality Act, which she said would "clarify that sex in the law means biological sex and not new, redefined meanings of the word".
Ms Badenoch, who believes this change would protect women and girls' spaces, hit back at the actor on X, formerly Twitter.
She said: "I will not shut up. I will not be silenced by men who prioritise applause from Stonewall over the safety of women and girls.
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