More than 1,800 people have died from the mosquito-borne viral illness, up from over 1,000 deaths reported last month in the year through March
Forty-seven people were rescued after the accident near Puerto Lempira, said Jose Domingo Meza, the armed forces spokesman.
Various boats have gathered off the Honduran coast for lobster-fishing season, which began this month and runs through February.
Another fishing boat capsized earlier in the day in the same region because of the poor weather, but all 49 people onboard were rescued, Meza said.
Honduras lobster exports generated $46 million in 2018, according to official data, and were sent mostly to the United States.