Army troops and personnel from the federal electricity authority have been deployed to the area on Mexico's eastern gulf coast to be on hand to help in emergencies.
The quake, the strongest to strike Mexico in more than 80 years, killed at least 61 people.
The hurricane center said that Katia's maximum sustained winds are now down to near 40 miles per hour (65 kph) and that it is expected to drift east of the Sierra Madre mountains as it peters out.
The government of Mexico issued a hurricane warning for the coast from Cabo Rojo to Laguna Verde and a tropical storm warning for Cabo Rojo north to Rio Panuco and south of Laguna Verde to Puerto Veracruz.
The storm has deluged the mountainous region in Veracruz, which has a history of deadly floods and mudslides.
Hurricane Katia has made landfall 20 kilometers from Tecolutla and hit as a Category 1. It then was downgraded to a tropical storm and forecasters expect it to dissipate Saturday.
Another report mentioned that Katia is believed to make a landfall by Friday evening or Saturday morning.
It may also hit the land around the same time as the expected landfall of Hurricane Irma in southern Florida, while another weather disturbance called Hurricane Jose which is now situated around 1,000 miles to the east is also expected to hit the same Caribbean islands that Irma plowed through this week.
Mexican soldiers who form part of the national disaster program patrol the coastway along the beach in Barra de Cazones, in Veracruz state, on September 7, 2017.
Hundreds of buildings were toppled across a number of southern states, with the hardest-hit being Juchitan and Oaxaca.