English tolerates the reversal of words in situations like this. It isn't necessary, but it isn't wrong to say, "The Foreign Affairs Ministry is on strike." Please, please correct.
Or better yet, the Foreign Ministry. This bug has been here, and has been reported, for years.
Or to use the actual term, the Foreign Office. It's great because it translates the Hebrew and it's an actual thing.
That might be the term in the UK. In Canada it is in fact Ministry of Foreign (or Global) Affairs; in USA it is the State Department.