The war your man fought in would have been the second Schleswig War.
This settled a tortuous border dispute between the rising,unifying, German states and Denmark. The 'Schleswig-Holstein question' is, to historians, a byword for impenetrable complexity.
The German military at this time was formed of individual state armies. Most likely your man was in the Prussian military, but you can find more out by checking the regiment. It could be he served with one of the smaller states.