Guatemalan authorities urged people to stay off the roads as floods hit several towns in eastern and northern Guatemala.
Civil Defense operations commander Sergio Cabanas said flooding was reported in Izabal and Peten provinces, and there were concerns about people staying in their homes.
"The problem is that people have refused to be taken to shelters, because they want to keep watch on their possessions" out of fear of looting if they evacuated, Cabanas said.
In recent months, Guatemala has been hit by heavy rains that have resulted in about 274 deaths and about $1.1 billion in damage to highways, infrastructure, homes and crops, according to government estimates.
In neighboring Belize, officials began evacuating people in three towns near the border with Guatemala after flood waters rose, said Peter Eden Martinez, the Cabinet representative in charge of emergency precautions for the flood-prone southern region.
Water levels on the Sittee River were rising by about a foot (30 centimeters) an hour, and officials expressed concern a key bridge could be washed out.
In Mexico, the country's National Water Commission said it was preparing for rains with efforts to widen and deepen channels below dams as needed. Southern Mexico has also been hit by severe flooding in recent months.
Matthew made landfall as a tropical storm Friday on Nicaragua's Caribbean coast and quickly crossed into Honduras. It toppled power lines and left thousands without power for hours in Honduras.
There were no immediate reports of major damage in Honduras, but thousands were evacuated. In Olanchito, near Honduras' northern coast, a creek overflowed and flooded a house but firefighters were able to rescue its 10 occupants.
Saturday afternoon, Matthew had maximum sustained winds of 35 mph (55 kph) and was moving inland toward Guatemala and southern Mexico at about 15 mph (24 kph).
The U.S. National Hurricane Center in Miami said Matthew could unleash 6 to 10 inches of rain, with as much as 15 inches possible in some areas in Belize, Guatemala and Mexico's Chiapas state.
In Honduras, authorities evacuated 300 people from small communities in the Gracias a Dios province, on the border with Nicaragua.
"A lot of rivers have high levels because of soil saturation due to frequent rains since May," said Randolfo Funez, operations director of the Contingencies Commission.
Authorities said that classes would be suspended until further notice and that 15,000 schools had been made available to be used as shelters.
Meanwhile, far out over the Atlantic, Hurricane Lisa weakened to a tropical storm and was drifting slowly north with maximum sustained winds near 70 mph (110 kph).