The US National Hurricane Center has downgraded Earl to a tropical storm.
The storm, which earlier had hurricane-strength wind speeds of up to 130km/h (80mph), made landfall early on Thursday in Belize, in Central America.
Earl weakened as it moved inland with wind speeds dropping to about 105 km/h.
The storm is predicted to move across northern Guatemala and south-eastern Mexico on Thursday, where its rains could still cause flash floods and mudslides.
Earlier, heavy rains fell on Honduras.
Residents of Belize City and other coastal communities had been urged by the authorities to move inland and take advantage of higher ground or a network of storm shelters.
Officials ordered the closure of the city’s international airport while archaeological reserves and national parks were shut.