In response to the current interest in CubeSats and potential applications for planetary exploration, this work studies the feasibility of using autonomous CubeSats to flyby near-Earth asteroids. Considering the limited performance of current propulsion systems for CubeSats, low-energy (impulsive and low-thrust) trajectories are designed to encounter near-Earth asteroids in the medium-fidelity Circular Restricted Three-Body Problem, and their existence in a high-fidelity ephemeris model is also verified. The use of large ground antennas for deep-space communications might represent a major portion of CubeSat mission budgets, and thus the feasibility of performing optical navigation to autonomously estimate and correct the trajectory of the CubeSat is also evaluated through Monte Carlo simulations. Preliminary results show that approximately 4 asteroids per year could be reached by a 3U CubeSat if deployed around the first or second Sun-Earth Lagrange points. According to the limited performance of current CubeSat components, flyby altitudes of the order of 100–500 kilometers are determined possible using only observations of the Sun and of the target asteroid for autonomous navigation.