We have discovered 20 dwarf Cepheids (DCs) in the Carina dwarf spheroidal galaxy from an analysis of individual CCD images obtained for a deep photometric study of the system. These short-period pulsating variable stars are by far the most distant (~100kpc) and faintest (V~23.0) DCs known. The Carina DCs obey a well-defined period-luminosity relation, allowing us to readily distinguish between overtone and fundamental pulsators in nearly every case. Unlike RR Lyrae stars, the pulsation mode turns out to be uncorrelated with light-curve shape, and the overtone pulsators do not tend toward shorter periods compared with the fundamental pulsators. Using the period-luminosity relations from Nemec, Nemec, & Lutz (1994, Cat. <J/AJ/108/222> and McNamara (1995AJ....109.1751M), we derive (m-M)_0_=20.06+/-0.12, for E(B-V)=0.025 and [Fe/H]=-2.0, in good agreement with recent, independent estimates of the distance/reddening of Carina. The error reflects the uncertainties in the DC distance scale, and in the metallicity and reddening of Carina. The frequency of DCs among upper-main-sequence stars in Carina is approximately 3%. The ratio of dwarf Cepheids to RR Lyrae stars in Carina is 0.13+/-0.10, though this result is highly sensitive to the star formation history of Carina and the evolution of the horizontal branch.