Authorities in the states of Veracruz, Tamaulipas and San Luis Potosi prepared for possible flooding and prepared evacuation shelters as rain pounded coastal and mountain regions. Tropical storm force winds extended as far as 205 miles (335 kilometers), but mainly east of the center, over the Gulf.
Officials said 6 inches (150 millimeters) of rain were possible in northern Veracruz state. Some isolated mountainous areas inland could get up to 15 inches (375 millimeters) of rain, the hurricane center said.
Forecasters said extreme south Texas also could get rain.
Arlene was projected to weaken later Thursday and dissipate on Friday.
The main threat to Mexico comes from heavy rains that could cause flash floods and mudslides in 13 states, the government said.
Rains could be welcome in Tamaulipas, where they would fall on soil dried out by the most severe drought to hit the area in 50 years. There was still unrepaired damage from Hurricane Alex, which struck the area as a Category 2 hurricane last year.