A 50-year-old retiree was examined and tested on July 2 at Eisenhower Army Medical Center, received antiviral treatment and recovered at home, according to a post news release.
A 21-year-old soldier was examined and tested July 4 and was not given medication.
A 16-year-old family member was seen on July 4 and was sent home to recover.
None were hospitalized and all three have fully recovered, the release said.
The tests were confirmed Wednesday by the Air Force School of Aerospace Medicine laboratory in San Antonio.
State and local public health departments have been notified.
The latest cases bring the total number of H1N1 cases at the Army post to 11.