Carlson is separately facing a lawsuit from a Jewish former producer on his show who alleges that staff fostered antisemitism in the office.
Carlson's "Tucker Carlson Tonight" is the highest-rated cable news program in the key 25-to-54 age demographic on the most-watched US cable news network.
The move comes after Fox News' Tucker Carlson spent months attacking minor brand changes to some of the characters as "woke."
Fox has argued that it had a right to report on election-fraud allegations made by Trump and his lawyers and that Dominion’s lawsuit would stifle press freedom.