Storm Katia has rapidly weakened after making landfall near the working-class beach resort of Tecolutla in the state of Veracruz on the Mexican Gulf coast.
Katia was downgraded from a hurricane to a tropical storm as it was about 175km northwest of Veracruz, Mexico with sustained winds of 70 km/h, the US National Hurricane Center (NHC) said.
Veracruz state officials said in a statement on Friday that the storm could cause landslides and flooding, and urged people living below hills and slopes to be prepared to evacuate.
Luis Felipe Puente, head of Mexico's national emergency services, said this week that Katia has "worrying characteristics" because it is very slow-moving and could dump a lot of rain on areas that have been saturated in recent weeks.
State oil and gas company Pemex has installations in and around the coast of Veracruz, but the firm has not reported any disruption to its operations.
Mexico is also dealing with the aftermath of a powerful earthquake on Thursday night. The quake, the strongest to strike the country in more than 80 years, killed at least 61 people.
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.
Millions of Florida residents were ordered to evacuate after the storm killed 21 people in the eastern Caribbean and left catastrophic destruction in its wake.
Hurricane Jose continued to gather strength far out in the Atlantic and was nearing Category 5 strength.
