The size distribution and total mass of objects in the Oort Cloud have important implications to the theory of planet formation, including the properties of, and the processes taking place in the early solar system. We discuss the potential of space missions, such as Kepler and CoRoT, designed to discover transiting exoplanets, to detect Oort Cloud, Kuiper Belt, and main belt objects by occultations of background stars. Relying on published dynamical estimates of the content of the Oort Cloud, we find that Kepler's main program is expected to detect between 0 and similar to 100 occultation events by deca-kilometer-sized Oort Cloud objects. The occultation rate depends on the mass of the Oort Cloud, the distance to its "inner edge," and the size distribution of its objects. In contrast, Kepler is unlikely to find occultations by Kuiper Belt or main belt asteroids, mainly due to the fact that it is observing a high ecliptic latitude field. Occultations by solar system objects will appear as a photometric deviation in a single measurement, implying that the information regarding the timescale and light-curve shape of each event is lost. We present statistical methods that have the potential to verify the authenticity of occultation events by solar system objects, to estimate the distance to the occulting population, and to constrain their size distribution. Our results are useful for planning of future space-based exoplanet searches in a way that will maximize the probability of detecting solar system objects, without hampering the main science goals.