In this letter, a novel procedure is introduced for the simulation of carbon nanotube (CN) antennas directly in the time domain. This formulation is based on the time-domain electric-field integral equation (TD-EFIE) for thin-wires, including external loads. Appropriate loads have been derived to match the physical response of single-walled CN media to external electromagnetic fields. The results show good agreement with a validated frequency-domain formulation. The time-domain formulation provides physical insight into the well-known characteristic effects of CN dipoles, such as slow-wave propagation and the existence of low-frequency resonances.