  We study M2-branes in $AdS_4\times S^7/{\mathbb Z}_k$ dual to 1/2 and 1/3 BPS
vortex loop operators in ABJM theory and compute their one-loop correction
beyond the classical M2-brane action. The correction depends only on the parity
of $k$ and is independent of all continues parameters in the definition of the
vortex loops. The result for odd $k$ agrees with the answers for the 1/2 BPS
Wilson loop in the $k=1$ theory and for even $k$ with the one in the $k = 2$
theory. Combining with the classical part, we find that the natural expansion
parameter seems to be $1/\sqrt{kN}$ rather than $1/\sqrt{N}$. This provides a
further setting where semiclassical quantisation can be applied to M2-branes
and produces new results inaccessible by other methods.
