The decision means Armstrong, who had planned to enter, will not participate. The race runs today through Sunday in Silver City. It would have been Armstrong's first competition since he broke his collarbone last month.
"Bummed (disappointed) to not be doing the Tour of the Gila in New Mexico," Armstrong wrote on his Twitter feed.
Brennan said he was bitter about the situation."From the UCI all the way down, we're all trying together to promote the sport of cycling," he said. "This doesn't do it. This leaves you with a real sour taste."
It was not immediately clear what was behind the decision by the UCI, cycling's international governing body. UCI officials did not immediately respond to e-mails seeking comment.
Brennan said Armstrong, the seven-time Tour de France winner, had planned to enter the 23rd annual Tour of the Gila in a buildup to the Giro d'Italia, which starts May 9.
Andy Lee, spokesman for USA Cycling, said the federation was not the source of the rule nor the decision to enforce it. "On the contrary, we would love to see Lance compete in the Tour of the Gila," Lee said. "It would be great for cycling in the United States."