The suspects opened fire and launched fragmentation grenades at soldiers when they arrived at the scene, the statement said.
The six suspects killed in the ensuing gun battle have yet to be identified and three others were arrested at the scene, the statement said. Authorities also seized 10 high-powered rifles, 12 fragmentation grenades and seven bulletproof vests.
Capt. David Mendoza died in the shootout and five other soldiers were treated at a local hospital and in stable condition Sunday.
The border state of Chihuahua, where Chihuahua city is located, has been plagued by drug violence as Mexico's crackdown on its powerful cartels stokes turf wars among traffickers.