Schools were ordered to stay closed and shelters have been set up in the states of Guerrero and Michoacan.
Carlos was downgraded to a tropical storm on Sunday, but meteorologists said it could again reach hurricane-level strength by Tuesday.
Guerrero was badly hit by Tropical Storm Manuel in September 2013, with thousands of people left stranded.
Guerrero state officials said more than 500 shelters were ready to receive residents.
Acapulco, the largest city in the state, closed its port.
The Miami-based US National Hurricane Center said that Carlos was 205km (125 miles) off the coast of Acapulco at 09:00 GMT on Monday, moving west-northwest at a speed of 9 km/h.
The storm had maximum sustained winds of 70mph (113km/h).
The Center warned that heavy rainfall could cause life-threatening flash floods and mudslides.
Following Tropical Storm Manuel, a mudslide swept through the village of La Pintada killing dozens of residents.
Residents of south-west Mexico are preparing for the arrival of Tropical Storm Carlos.