  In the context of $2+1-$dimensional gravity coupled to a particular nonlinear
electrodynamics (NED), we obtain a class of traversable / Morris-Thorne type
wormhole solutions. The problem is reduced to a single function dependence in
which the shape function acts as generator to the wormholes. The field ansatz
is pure magnetic and the nonlinear Lagrangian is $\sqrt{F_{\mu \nu }F^{\mu \nu
}}$ i.e. the square root of the Maxwell Lagrangian. In $2+1-$dimensions the
source-free pure magnetic non-linear Maxwell equation with square-root
Lagrangian is trivially satisfied. The exotic energy density is found
explicitly and the flare-out conditions are emphasized.
