The Ocean Lion's captain ordered Igor Yavorskyy, 27, to investigate an incident of intoxicated crew mates at 5:30 p.m. Friday.
Later Friday night, a red, blood-like substance was found on the main deck, and Yavorskyy was missing, the (New Orleans) Times-Picayune reported.
The Plaquemines Parish Sheriff's Office then obtained a search warrant, but was unable to find the missing crew member, the newspaper said.
Possible blood evidence was found on crew members clothing and in a living quarters, the sheriff's office said.
The FBI, the Plaquemines Parish Port Authority, the U.S. Coast Guard and U.S. Customs and Border Protection were assisting in the investigation.
The Ocean Lion is anchored near Braithwaite, La., in Plaquemines Parish.