1970 as colloquial shortening for improvisation. The famous New York City comedy club, founded in 1963, was, in full, The Improvisation.
Entries linking to improv
improvisation n.
"act of improvising musically," 1786, from French improvisation, from improviser "compose or say extemporaneously" (17c.), from Italian improvisare "to sing or speak extempore," from Latin improviso "unforeseen; not studied or prepared beforehand," ablative of improvisus "not foreseen, unexpected," from assimilated form of in- "not, opposite of" (see in- (1)) + provisus "foreseen," also "provided," past participle of providere "foresee, provide" (see provide). From music the sense expanded to a general meaning "do or perform on the spur of the moment."