The man, belonging to the India Reserve Batallion, had left for Kavaratti by ship from Kochi on January 3 and tested positive on Monday, official sources said. He is not a resident of the islands, they said.
The case was reported two weeks after the Lakshadweep administration revised Standard Operating Procedures by doing away with mandatory quarantine guidelines for those arriving from Kochi.
The islands had so far not reported a single positive Covid-19 case.
Taking measures to prevent the spread of the virus, the administration has directed all those who had come in contact with him to go on quarantine, they said.
The samples of his primary contacts have been taken for lab examination, officials said.
The administration also suspended all the inter island movements, including ships from Tuesday, they said.
It had recently relaxed the SOP.
In a communication, the administration had said anyone can now visit the islands from the mainland with a negative test report of RT-PCR obtained 48 hours before travel.