The theory of quantum order-by-disorder (QOBD) explains the formation of modulated magnetic states at the boundary between ferromagnetism and paramagnetism in zero field. PrPtAl has been argued to provide an archetype for this. Here, we report the phase diagram in magnetic field, applied along both the easy a axis and hard b axis. For field aligned to the b axis, we find that the magnetic transition temperatures are suppressed and at low temperature there is a single modulated fan state, separating an easy a axis ferromagnetic state from a field polarized state. This fan state is well explained with the QOBD theory in the presence of anisotropy and field. Experimental evidence supporting the QOBD explanation is provided by the large increase in the T^{2} coefficient of the resistivity and direct detection of enhanced magnetic fluctuations with inelastic neutron scattering, across the field range spanned by the fan state. This shows that the QOBD mechanism can explain field induced modulated states that persist to very low temperature.