Barry was about 55 miles east-northeast of Veracruz with maximum sustained winds of 45 miles per hour and higher gusts, the National Hurricane Center in Miami said in its 7 p.m. CDT advisory.
A tropical storm warning was in effect for Punta el Lagarto to Tuxpan, Mexico.
Barry was moving westward at about 6 miles per hour. Further movement to the west was expected with a decrease in forward speed over the next 24 hours. The storm could strengthen before making landfall Thursday morning, then weaken after the center crosses the coast.
Tropical-storm-force winds extended up to 70 miles from the center of the storm.
The hurricane center warned of the potential for life-threatening flash floods and mudslides, especially in mountainous areas. Barry was expected to produce 3-5 inches of rain across southern Mexico, with localized amounts of 10 inches possible.