Conservatives and Trump campaigners had claimed last year that the US company had altered its voting machines to deny re-election to Donald Trump.
The false claim of a stolen election was promoted by Mr Trump and helped fuel the 6 January attack on Congress.
Fox News said it would fight the "baseless lawsuit in court".
The lawsuit argues that Fox News, which hosted guests touting anti-Dominion conspiracy theories during the 2020 election, "recklessly disregarded the truth" because "the lies were good for Fox's business".