The case involved a woman living in Cameron County near the Mexico border who is not pregnant, the Texas Department of State Health Services said.
Pregnancy is the biggest concern with Zika because the virus can cause severe, life-long birth defects, including microcephaly, in which a child is born with an abnormally small head, a sign its brain has stopped growing normally.
Texas said it currently has no other suspected cases of local Zika transmission, but officials there plan to step up efforts to watch for the virus.