Richards, a fiesty Democrat who was governor from 1991 into 1995, was reported to be doing well, reports the Austin American-Statesman.
Richards lost her 1994 gubernatorial re-election bid to George W. Bush. She became nationally known after the 1988 Democratic National Convention where she said Bush's father, the first President Bush, was born with a "silver foot in his mouth," the report said.
The Houston facility will determine a treatment plan after tests to determine the extent of the cancer.
One expert said treatment for cancer of the esophagus, which carries liquid and food to the stomach, has improved in recent years. He said up to 90 percent of patients can survive if the cancer is caught early.
Cathy Bonner, a businesswoman who had worked in the Richards' administration, said, "Whatever it is, she'll face it with courage and conviction."