The sub-contractor was working on a maintenance platform, alongside a jetty at Milford Haven port, when it collapsed at 1500 BST on Saturday.
He is believed to be a 44-year-old Dutchman. His family have been informed.
Seven men were rescued and one man is "stable" in hospital.
South Hook LNG said they have been unable to remove the man's body so far because of the jack-up barge's instability.
Dyfed Powys Police said: "Every effort is being made to recover the body, which is believed to be a 44-year-old Dutch national."
A South Hook LNG spokesperson confirmed the death with "deep regret" and said next of kin had been informed.
"Our thoughts and sympathies are with his family," said the spokesperson.
Capsize
"We can confirm that all the other individuals on the barge are accounted for and are safe.
"The relevant authorities are in attendance at the scene and an investigation is underway."
Five men were rescued by boat from the jack-up barge, and two were pulled from the water.
The floating jack-up barge is a four-legged platform.
The Health and Safety Executive (HSE) has launched an investigation at the terminal, which is being built at Milford Haven.
Coastguard crews, police, fire and ambulance teams joined Milford Haven Port Authority in the search for the missing man until it was called off late last night.
Dyfed-Powys Police said it suspended the operation due to weather conditions last night but the search resumed on Sunday using a remote vessel.
Specialist divers were unable to enter the water for safety reasons.
Milford Haven Port Authority (MHPA) established an exclusion zone around the barge, which is listing heavily, amid fears it could capsize.
But the port was able to reopen on Sunday afternoon.
There is a 2,000 litre diesel tank in the water, but this is currently intact, said a police spokesman.
The Environment Agency and MHPA are monitoring the situation and an anti-pollution vessel is at the scene.
There has been no risk to the general public throughout this incident, the spokesman added.
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