CBS News' Houston affiliate KHOU-TV says that there have been no injuries reported, but the storm destroyed trailer homes, peeled the roofs off buildings, and blew out windows in some downtown Houston skyscrapers.
High winds, heavy rain, and lightning swept across the area beginning at about 6 a.m. CT, but the worst appeared to be over by 9 a.m.
The storm knocked out power to about 160,000 residential and commercial customers but transmission lines were not affected, the local electrical utility said.
The power outages appeared to be concentrated north of the I-10 freeway that runs through the city from east to west, said Reliant Energy HL&P spokeswoman Leticia Lowe.
Lowe said crews were working to restore power and hoped to have most customers connected again by midday.
Jim White of the Harris County Emergency Management Office said flooding had occurred in some low-lying areas.
Fallen tree limbs, flooded roads, and traffic light outages caused long delays for people driving to work.
The loss of electric power also led many schools in the area to cancel classes for the day.
In other areas of Texas, twisters were spotted Sunday evening through Monday morning, with minor damage reported.