A fishing vessel with 82 crew members capsized because of the storm, but they were all rescued, an official with Honduras' Copeco emergency services agency told the HCH television channel.
The red alert for the Bay Islands, an archipelago of eight main islands and smaller cays, was to last two days.
The islands' main airport in Roatan was closed, as were two others near the Caribbean coast on the mainland.
Schools were also shut in the north of the country.
Tropical Storm Earl, packing winds of up to 118 kilometers per hour, was expected to drive into northern Honduras, a coastal part of neighboring Guatemala, and the small country of Belize.
Authorities have warned of high winds, heavy rain and flooding.