We study the real-time dynamics of the order parameter <σ(t)> in the Ising field theory after a quench in the fermion mass, which corresponds to a quench in the transverse field of the corresponding transverse field Ising chain. We focus on quenches within the ordered phase. The long-time behavior is obtained analytically by a resummation of the leading divergent terms in a form-factor expansion for <σ(t)>. Our main result is the development of a method for treating divergences associated with working directly in the field theory limit. We recover the scaling limit of the corresponding result obtained for the lattice model. Our formalism generalizes to integrable quantum quenches in other integrable models.