In my dialect of English (western USA), "to take leave" means "to say goodbye and depart". "To take a leave" means "to be absent from military duty". We would never use these expressions for taking time off of work.
Here in the UK we definitely say 'take leave' or 'take some leave' but never 'take a leave'. I'm curious though, as I note that both the commenters saying 'a' is required have South Asian names - is 'take a leave' how it's said in Indian English?
No, "take leav" (no article) is fine; at least i (who speak American English) find it more idiomatic than "take a leav" (with article). (Brits et al. might find "take a leav" [with article] more idiomatic.)