"There are over 200 species of malaria. Humans are infected by five. But birds, bats, lizards and antelopes are also hosts for malaria parasites." [1]

So no, unfortunately, curing all the humans will not wipe out malaria. The only real solution is to drive the mosquito vector to extinction, everything else is a temporary half-measure.

[1] https://www.abc.net.au/radionational/programs/scienceshow/ma...