Mexico's defence department said the suspects had attacked an army patrol on a highway outside the city.
It said six suspected drug cartel members and one soldier were killed in a separate series of clashes on Tuesday farther west along the border. At least 10 soldiers and a police officer were injured in those clashes.
Spiralling drug violence
The US consulate in Matamoros has posted a message on its website advising US citizens to be aware of the recent violence.
"The US Consulate General in Matamoros has restricted the travel of American officials to Reynosa until further notice," the statement read, dated Wednesday.
The government of Felipe Calderon, the Mexican president, has deployed more than 49,000 troops across the country as part of its war on drugs.
However, broad daylight shootings are common and killings by drug gangs soared to an unprecedented 7,000 last year alone as rival groups fought over markets and control of smuggling routes into the US.
More than 15,000 people have died in the spiralling drug violence in the past three years in Mexico.