Cole Ford, 31, whose three-year NFL career ended in 1997 after he missed crucial kicks, was identified earlier by police as the owner of a white minivan from which shots were fired at the entertainers' compound.
No one was hurt, but police said shotgun pellets shattered windows and left a hole in a wall. Police have not said if the two were at home at the time.
Ford was captured without incident Tuesday afternoon at a copy store near the Las Vegas Strip after a woman tipped police that he was inside, police said.
He faces six felony warrant charges of discharging a firearm from a motor vehicle and two felony counts of assault with a deadly weapon.
The long-running Siegfried & Roy show was forced to close a year ago after Horn suffered a near-fatal tiger mauling during a performance.