My wife asked me that this morning. Initially I was fairly certain that there was one, but upon reflection I realized there is no equivalent. ("One-track specialist” is about as close as we get in English, but that is not quite the same.)
It is another example of handy compound words in German which somehow become popular take on a life of their own in the German language. Here is a very basic example, in English we have the noun “glove,” but in German the word for glove is the compound word “Handschuh” -- literally hand-shoe. I suspect most native German speakers never even think of Handschuh as a compound word.
These compound words are highly useful, and a few have even been adopted into modern English. “Zeitgeist,” “Kindergarten,” and “Weltschmerz” would be examples. So back to Fachidiot, literally it means subject-idiot. A Fachidiot is a person who is an expert in his or her specialty, but is clueless and foolishly indifferent as to how his/her actions affect others.
For example, a governmental agency sends a technical consultant to a hospital ward to improve efficiency. He devises a system which identifies various procedures the registered and practical nurses perform. Each nurse is then required to input each performed procedure into a computer database. In theory, this improves efficiency by giving supervisors an overview and makes billing highly accurate. In practice, the nurse wastes a couple of hours each day inputing stats into a computer, which reduces the time she/he spends performing her/his specialty (nursing), and reduces the level of patient care.
The German language also has a wonderful word which describes the above situation, “Verschlimmbesserung.” This compound word describes a situation in which the solution makes the situation worse.
Yes these compound words are great, but I must admit, sometimes they are mindbogglingly difficult when learning the language. For example, the German word for speed limit is "Geschwendigkeitsbegrenzung," but thankfully in the late 20th century they also adopted “Tempolimit.” Some of you may remember the compound word “Fahrvergnügen” from the old VW commercials in English – that literally means “driving pleasure.”
Photo is from Pixabay with effects and text by 
