A warning issued by the department covers the peninsula from Chetumal, Mexico, northward to Tulum, including the island of Cozumel.
Ernesto is expected to make landfall overnight or in the early hours Wednesday, with heavy rains and strong winds likely to affect transportation routes and telecommunication systems. There could also be flooding and mudslides.
The department says other services that may be affected include emergency and medical care, as well as water and food supplies.
Ernesto strengthened from a tropical storm earlier Tuesday, and the U.S. National Hurricane Center said it had winds of 129 kilometres an hour by late afternoon.
The hurricane was centred about 225 kilometres east of Chetumal.