We present the results of near-infrared observations of extragalactic Cepheids made with the Near-Infrared Camera and Multi-Object Spectrometer on board the Hubble Space Telescope (HST). The variables are located in the galaxies IC 1613, IC 4182, M31, M81, M101, NGC 925, NGC 1365, NGC 2090, NGC 3198, NGC 3621, NGC 4496A, and NGC 4536. All fields were observed in the F160W bandpass; additional images were obtained in the F110W and F205W filters. Photometry was performed using the DAOPHOT II/ALLSTAR package. Self-consistent distance moduli and color excesses were obtained by fitting period-luminosity relations in the H, I, and V bands. Our results support the assumption of a standard reddening law adopted by the HST Key Project on the Extragalactic Distance Scale. A companion paper will determine true distance moduli and explore the effects of metallicity on the Cepheid distance scale.