At cryogenic temperatures, organic single-photon sources (SPSs) offer Fourier-limited emission, virtually unlimited photostability, and emission wavelengths selectable by molecular design, making them attractive for quantum metrology, secure communication, and photonic quantum information processing. However, their efficient integration with photonic microstructures has remained challenging, limiting photon collection from single organic emitters under cryogenic operation. Here, we demonstrate a cryogenic planar metallo-dielectric antenna that efficiently directs the emission of a single dibenzoterrylene (DBT) molecule towards the collection optics. The device reaches a collection efficiency of 97% and delivers 100 million photons per second into the first lens. We measure a photon indistinguishability for the Fourier-limited transition of 91.2% while maintaining a high single-photon purity of 97.7% under strong continuous-wave (CW) and pulsed excitation. These results establish organic molecules as a high-performance platform for single-photon generation and represent an important step towards scalable organic quantum photonic technologies.