Armstrong, who was stripped of his seven Tour de France victories and banned for life last year before admitting to doping, withdrew from the meet shortly after organisers informed his agent Bill Stapleton that FINA had ruled him ineligible.
American Armstrong and meet organisers did not respond to requests for a comment.
FINA said in a statement that athletes convicted of doping offences were not allowed to enter competitions sanctioned by the world swimming body.
"Therefore, FINA wrote a letter to the US Masters Swimming (with copy to US Aquatic Sports and USA Swimming) requesting not to accept the entry of Mr. Lance Armstrong in the above mentioned competition," it said on its website.
The Statesman newspaper reported earlier that Armstrong had planned to take part in the Masters South Central Zone swimming championships in the Texan state capital.
It quoted Rob Butcher, the executive director of Masters swimming, as saying nobody had filed a grievance against Armstrong competing in an event that does not come under the umbrella of the US Anti Doping agency.
Media reports said Armstrong had been due to compete in the 500-, 1,000- and 1,650-yard freestyle races in his home city.
Masters swimming is open to anyone aged over 18 and is popular with triathletes.
- Swimming & Diving
- Sports & Recreation
- Lance Armstrong