More than 60 people were killed, at last count.
Tropical storm warnings are also announced in the northern part of Cabo Rojo to Rio Panuco as well as the southern areas of Laguna Verde to Puerto Veracruz.
The National Hurricane Center is warning that "this rainfall will likely cause life-threatening flash floods and mudslides, especially in areas of mountainous terrain".
The country has been dealing with the arrival of the Gulf coast hurricane while parts of it are already in ruins following a magnitude 8.1 quake.
Katia transitioned from a tropical storm to a hurricane on Wednesday afternoon, and was a Category 2 hurricane as of 4 p.m. Friday, with sustained wind speeds of 105 miles per hour.More news: Paterno admitted to hearing earlier complaint about Sandusky sexual abuse
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The eye of Hurricane Irma, center, hovers just north of the island of Hispaniola, with Hurricane Katia, left, in the Gulf of Mexico, and Hurricane Jose, right, in the Atlantic Ocean, in a satellite image taken at 11:15 a.m. EDT on Sep. 7.
Hurricane Katia has deteriorated into a soggy tropical depression that is dumping rain over the mountains of east-central Mexico. Forecasters said it could become a major hurricane by the time in hits land on Saturday. Katia made landfall Friday night as a hurricane.
As Katia was making landfall, Hurricane Irma, one of the most powerful Atlantic storms in a century, walloped Cuba's northern coast as a Category 5 storm.
It made landfall near beach resort of Tecolutla in Veracruz.
Mexico is also dealing with the aftermath of a powerful quake on Thursday night.