Don Lewis's family are also offering a $100,000 (£76,300) reward for information about what happened to him when he vanished in 1997.
The lawsuit, filed by Mr Lewis’s three surviving daughters, is an attempt to force Baskin to submit evidence on the record.
Mr Lewis disappeared a day before he was scheduled to travel to Costa Rica. He was declared legally dead in 2002.
Baskin, 59, set up an animal sanctuary with her then-husband in Tampa, Florida.
It later became the Big Cat Rescue sanctuary which, in turn, gained worldwide renown through the hit Netflix series about private zoo operator Joe Exotic.
Conspiracy theories surrounding Mr Lewis’s fate featured prominently in the documentary, including suggestions that Baskin – who received the bulk of his of his £4.5 million estate – was responsible for his disappearance.
She and Mr Lewis were married at the time of his disappearance, but he had filed for a restraining order against her two months earlier.
She has categorically denied any involvement in his presumed death. No-one has ever been arrested over his disappearance.
Speaking at a press conference on Monday, Mr Lewis's youngest daughter Gale Rathbone said Tiger King had revived interest in the case.
"Amazingly, our little family tragedy has become your tragedy," she said. "Our search for closure and truth has become your mission also.
Baskin told The Associated Press: "It's been my policy not to discuss pending litigation until it's been resolved.
"I had told some news outlets that I thought the press conference on August 10 was just a publicity stunt, but at that time was not aware there would be pending litigation."