We study fixed loci of antisymplectic involutions on projective hyperkähler manifolds of \({\mathrm {K}}3^{[n]}\)-type. When the involution is induced by an ample class of square 2 in the Beauville–Bogomolov–Fujiki lattice, we show that the number of connected components of the fixed locus is equal to the divisibility of the class, which is either 1 or 2.