The magnon-photon interaction is formulated for a direction of the magnetic vector of the electromagnetic wave perpendicular to the direction of the sublattice magnetization in an antiferromagnet, and from this the one-magnon self-energy is calculated. The linewidth predicted from the one-magnon one-photon process is in good agreement with the experimental value for Mn${\mathrm{F}}_{2}$. Higher-order magnon-photon scattering processes are indicated and the corrections arising from such multiple magnon-photon scattering processes are found to depend on temperature and microwave power.