Polaritons are light-matter quasiparticles that govern the optical response of quantum materials at the nanoscale, enabling on-chip communication and local sensing. Here, we report Landau-phonon polaritons (LPPs) in magnetized charge-neutral graphene encapsulated in hexagonal boron nitride (hBN). These quasiparticles emerge from the interaction of Dirac magnetoexciton modes in graphene with the hyperbolic phonon polariton modes in hBN. Using infrared magneto-nanoscopy, we reveal the ability to completely halt the LPP propagation in real space at quantized magnetic fields, defying the conventional optical selection rules. The LPP-based nanoscopy also tells apart two fundamental many-body phenomena: the Fermi velocity renormalization and field-dependent magnetoexciton binding energies. Our results highlight the potential of magnetically tuned Dirac heterostructures for precise nanoscale control and sensing of light-matter interaction.