This paper considers an integrated sensing and communication (ISAC) system with monostatic radar functionality using a zero-padding orthogonal frequency division multiplexing (ZP-OFDM) downlink transmission. We focus on ISAC's sensing aspect, employing an energy-detection (ED) method. The ZP-OFDM transmission is motivated by the fact that sensing can be performed during the silent periods of the transmitter, thereby avoiding self-interference (SI) cancellation processing of the in-band full duplex operation, which is needed for the cyclic prefix (CP)-OFDM. Additionally, we also show that ZP-OFDM can reject nearby clutter interference. We derive the probability of detection (PD) for the ZP and CP-OFDM systems, allowing useful performance analyses. In particular, we show that the PD expressions lead to an upper bound for the ZP-OFDM transmission, which is useful for selecting the best ZP size for a given system configuration. We also provide an expression that allows range comparison between ZP and CP-OFDM, where we consider a general case of imperfect SI cancellation for the CP-OFDM system. The results show that when the ZP size is 25% of the fast Fourier transform size, the range loss of the ZP system range is only 17% larger than the CP transmission.