More than 8,000 customers are without power in Texas City and La Marque, according to Texas New Mexico Power.
The outage began at about 5:30 p.m.
At 8:40 p.m., a company spokesman said the company estimated that full power would be restored around midnight.
Most of the outages are in Texas City, in an area between Interstate 45, FM 1764 and state Highway 146.
In La Marque, the outage has knocked out some lights at intersections, the city said. Police urged drivers to use caution while driving.
The exact cause of the outage was not immediately clear.
Crews were working on routing power around the problem and restoring service as quickly as could be done safely, the company said. The work was "slow and methodical," Texas New Mexico Power spokesman Eric Paul said.
Some power companies, including Entergy, which serves the Bolivar Peninsula, asked customers to conserve power on Wednesday night because of expected heavy demand on the power grid. It's unknown whether heavy demand caused the power outage in Texas City and La Marque.
Temperatures tonight are expected to be near or below freezing across Galveston County.