The show is filmed in Hawaii, which is bracing itself after an 8.8-magnitude earthquake off Chile earlier.
Writing on Twitter, the show's executive producer Carlton Cuse said: "To ALL on the LOST crew -- responding to the Tsunami warning -- safe refuge is available at the studio."
He added: "Waves to reach Hawaii just after 11AM."
Actress Carrie Preston, who is married to Lost star Michael Emerson, reassured fans that she and her husband are in mainland America.
"Michael and I are safe in LA and praying the tsunami doesn't hit the islands too hard!" she wrote. "Thanks for the concern."
Meanwhile, the show's co-creator Damon Lindelof posted: "Praying for Chile and all the islands of Hawaii. Please send our cast and crew all your positive energy."