Search and rescue teams and generators were headed to the area of Idabel, a town of about 7,000 in southeast Oklahoma, he tweeted.
"Storms hit in Bryan, Choctaw, and Le Flore counties, among others. Additional flash flooding in some areas," he said.
The National Weather Service had issued tornado warnings for parts of Texas, Oklahoma and Arkansas.
Tornadoes are a frequent and often devastating weather phenomenon in the United States, with the Great Plains states of Kansas, Oklahoma and Texas the hardest hit.
In December last year, dozens of devastating tornadoes ripped through five US states overnight, leaving at least 79 people dead in Kentucky -- with fatalities also recorded in Tennessee, Arkansas, Missouri and Illinois.