Hanna, the first of the 2020 Atlantic hurricane season, made two landfalls on Saturday afternoon and evening in southern Texas, reports Xinhua news agency.
It weakened into a tropical storm early Sunday morning and moved toward northern Mexico, the National Weather Service said.
A flash flood and tornado watch are in effect in parts of the area until Sunday night.
Texas Governor Greg Abbott on Saturday issued a disaster declaration for 32 counties, calling for residents not to forget the existing threat of the COVID-19 pandemic.
"This challenge is complicated and made even more severe seeing that it is sweeping through an area that is the most challenged area in the state for COVID-19," he said.