Hanna landed on Father Island on Saturday and is now beating the area between Corpus Christi and Brownsville.
With winds of up to 85km / h (137km / h), the storm ripped the roofs from houses.
Hanna is currently a category 1 hurricane, the lowest level on the Saffir-Simpson scale in five stages.
“Any hurricane is a huge challenge,” Gov Abbott said on Saturday. “This challenge is complicated and made even more serious, as it is going through an area that is the most challenged area in the state for Covid-19.”
The National Hurricane Center (NHC) has warned that “a life-threatening storm wave will continue along parts of the Texas coast from Port Mansfield to Sargent.”
He called on local residents to follow the advice provided by the emergency services.
According to the chronicle of the Houston Chronicle, the storm is expected to mainly bypass the Houston region.
Hanna hits Texas while the southern state is struggling to contain the coronavirus epidemic.