An ordinance is a municipal or county law. Ordnance is a mass noun referring to military materials such as weapons, ammunition, equipment, and vehicles.
Although ordinance and ordnance now share no definitions, they both come from the Middle English ordinaunce, meaning to set in order. A third word, ordonnance, which still appears occassionally, began as a variant of ordinance but has since taken a meaning of its own—namely, the arrangement of parts in a building, picture, or literary work.
Examples
Ordinance
Under the Los Angeles medical marijuana ordinance, only those dispensaries that registered with the city by Nov. 13, 2007, will be allowed to operate. [LA Times]
Allegheny County Council on Wednesday voted not to take action on a proposed ordinance that would have required the county executive to take a leave of absence while he runs for governor. [Post-Gazette]
Ordnance
Even now, doctors in Misrata are reporting an uptick in amputations, a common result of unexploded ordnance. [The Atlantic]
The U.S. Atlantic Fleet stores, maintains and loads bombs, missiles and other ordnance at this base. [US Navy Seals blog]