The CDC said H9N2 is the most commonly identified avian flu virus in Vietnam.
Today's announcement raises the number of affected states to 8.
Seven states have now reported the virus in dairy herds, with detections at 21 facilities.
The patient lived adjacent to a poultry market, but there were no reports of bird illnesses or deaths.
The virus is a reassortant between the older H5N1 clade (2.3.2.1c), still circulating in parts of Asia, and a newer H5N1 clade (2.3.4.4b) that began circulating globally in 2021.
The outbreak in Texas will prompt the culling of about 1.6 million layer hens, as Michigan marks its fourth outbreak at a commercial farm.
The nasopharyngeal swab didn't suggest upper respiratory involvement, and virus sequencing of the eye sample showed one change that isn't linked to transmission.
The virus was also confirmed on five more Texas farms, as investigators find more clues from animal samples and genetic sequences.
The patient's only symptom is conjunctivitis, which has been seen before in avian flu infections.
Some states have already tightened their requirements for importing dairy cattle from affected states.