The organization wants the court to make absentee voting available to all eligible voters in the state.
The group and its state organization filed its lawsuit Friday in state court against Gov. Bill Lee, Secretary of State Tre Hargett and elections coordinator Mark Goins.
Tennessee requires voters to give an excuse for voting by absentee ballot.
Tennessee has multiple elections this year, including a statewide election on Aug. 6 and the general election on Nov. 3.
The ACLU said in a news release that without a vaccine, social distancing and avoiding groups are among the only measures known to protect against the spread of the virus. Some other states have made vote by mail and absentee voting available, said Dale Ho, director of the ACLU’s Voting Rights Project.