Optical excitation of stripe-ordered La_{2-x}Ba_{x}CuO_{4} has been shown to transiently enhance superconducting tunneling between the CuO_{2} planes. This effect was revealed by a blueshift, or by the appearance of a Josephson plasma resonance in the terahertz-frequency optical properties. Here, we show that this photoinduced state can be strengthened by the application of high external magnetic fields oriented along the c axis. For a 7 T field, we observe up to a tenfold enhancement in the transient interlayer phase correlation length, accompanied by a twofold increase in the relaxation time of the photoinduced state. These observations are highly surprising, since static magnetic fields suppress interlayer Josephson tunneling and stabilize stripe order at equilibrium. We interpret our data as an indication that optically enhanced interlayer coupling in La_{2-x}Ba_{x}CuO_{4} does not originate from a simple optical melting of stripes, as previously hypothesized. Rather, we speculate that the photoinduced state may emerge from activated tunneling between optically excited stripes in adjacent planes.