Neither. The order is from a German customer.

Neither of them... you should use the article 'a' before 'German customer'

The second one is correct, you just need to add "a" which is the article before "German customer". "Germany" is the name of the country and is therefore a proper noun, but it does not describe the people who live in that country. I am from Australia, but if you were talking about me you would describe me as Australian. Similarly, you are describing a customer as opposed to giving us the name of the country in which he lives, which means you use "German", not "Germany". I hope this helps.