PM's can be found in all types of industries. In regards to PM of technical fields, most people were promoted from an engineering type position (with engineering degrees).
I "only" have an ME degree, but have surpassed many in my company who have undergrad and graduate business degrees due to the type of work that occurs in my company (automotive).
OP, if you want to go into a very technical industry, the engineering degree will definitely help. If you are a PM for a internet promotions company making online ads, anybody with a degree and strong organizational skills will succeed.