1940s (originally US): blend of fan² and magazine.

• fan from Old English:

  The spelling fan can represent two quite different words. The first, meaning ‘a device to create a current of air’, goes back to the Old English noun fann, a word of Latin origin. It was a device for blowing air through harvested grain to winnow it, removing the husks or chaff from the seed. The second fan, meaning ‘enthusiast, supporter’, is short for fanatic (mid 16th century). Its earliest uses are recorded from the end of the 17th century, but it became particularly established in American English during the 19th century. In Latin fanaticus meant ‘inspired by a god’ and came from fanum meaning ‘a temple’. In its first English appearances fanatic was used as an adjective to describe the kind of frenzied speech or behaviour typical of someone possessed by a god or demon. As a noun it originally meant ‘a mad person’ and then ‘a religious maniac’. Fanzine was coined in the 1940s in the US for a magazine produced by amateur enthusiasts of science fiction, though fanzines are now often about music, film, or sport. The word is a blend of fan and magazine.