Mexican President Claudia Sheinbaum said emergency protocols were activated but that neither Chiapas nor the neighbouring state of Tabasco reported issues, and Guatemalan President Bernardo Arevalo said there were no deaths.
In some parts of Guatemala, residents in their homes and office workers spilled onto the streets.
The quake struck at a depth of 15.2km, the US Geological Survey said, after revising its earlier assessment of a magnitude 7.4 quake at a shallow depth of 10km.
There were at least10 aftershocks between magnitude 4.9 and 6.0, according to USGS.
Following the tremor, the US Tsunami Warning System said hazardous tsunami waves were possible along coasts located within 300km of the epicentre, which was in the sea 58km from the small coastal town of Puerto Madero.
The waves could reach levels between 30cm and one metre above tide level for some coasts in Mexico and Guatemala, the tsunami warning centre said.
Mexico's secretary of the navy Raymundo Morales said water levels were not expected to rise more than half a metre but nevertheless advised people to stay away from beaches for now.
"There is no problem, no serious maritime impact," Morales said during a regular government press conference.
"We only expect some beaches to see a rise in water level of up to half a meter due to the tsunami effect from the earthquake."
A series of aftershocks, including some with magnitudes between 5.0 and 6.0, was also felt in Mexico, Guatemala and El Salvador.
In Guatemala City, the earthquake shook buildings and prompted some residents to dash from their homes onto the street, according to a Reuters witness.
Local media in Guatemala showed footage of staff leaving a government building as security protocols were activated.
"I got really scared and it reminded me of the recent earthquake in Venezuela. So I ran out and went down the stairs because I live on the eighth floor. The shaking wouldn't stop," Alexander Valdez, a 29-year-old accountant, told Reuters in Guatemala City.
Adolfo Zacarias, a 43-year-old customer service worker who lives on the third floor of his building, said he sought shelter under a structural column as the shaking began.
"I think the memories of what recently happened in Venezuela came back to us and that scared us a lot," Zacarias said.
Venezuela is still reeling from twin earthquakes that struck the country on June 24, when magnitude 7.2 and 7.5 tremors hit within less than a minute of each other in the north-central region, toppling buildings in Caracas and nearby coastal areas and triggering a prolonged rescue and relief effort.
