I don't know that anybody offers a Masters degree specifically in "search engines", but loosely speaking the main academic field backing most search engines is "Information Retrieval"[1].
You can get a taste of the kinds of things covered in this field by looking at this class site (among many others)
https://web.stanford.edu/class/cs276/
That said, to build a modern competitive search engine, you'll need to look into software engineering, distributed systems, artificial intelligence, machine learning, linguistics, computer vision, signal processing, graph theory, databases, scheduling, machine translation, and FSM-only-knows what else.