Wordorigins.org

On the fritz is rather mysterious in origin. Merriam-Webster gives a date of first use of 1902, but doesn’t provide a citation. Roy McCardell’s 1903 Conversations of a Chorus Girl also uses it:

They gave an open air [performance] that put our opera house show on the Fritz.

The phrase is often popularly associated with the world wars and the fact that the Germans were nicknamed Fritz by the Allies in both wars. It’s commonly thought that the phrase has its origin in things German and bad, but as we can see this is not the case. The phrase appears well before the First World War.

(Sources: Historical Dictionary of American Slang; Merriam-Webster’s Collegiate Dictionary, 11th Edition)