In a typical experiment in magnonics, thin films are magnetized in plane and spin waves only carry angular momentum along their spatial propagation direction. Motivated by the experiments of Bozhko et al. [Phys. Rev. Research 2, 023324 (2020)], we show theoretically that for obliquely magnetized thin films, exchange-dipolar spin waves are accompanied by a transverse spin current. We propose an experiment to electrically detect this transverse spin current with Pt strips on top of an yttrium iron garnet film, by comparing the induced spin current for spin waves with opposite momenta. We predict the relative difference to be of the order 10−4, for magnetic fields tilted at least 30∘ out of plane. This transverse spin current is the result of the long-range dipole-dipole interaction and the inversion symmetry breaking of the interface.