"If testing goes well, as soon as next month," Musk wrote on social media.
Earlier in the day, Musk said damage in the booster propulsion section appears to be minor but they still need to inspect all the engines.
SpaceX conducted an ignition test on Monday of the spacecraft's booster, which is powered by 33 Raptor engines, but it ended in a powerful explosion that started a fire at the bottom of the launch tower.
Starship is a fully reusable two‑stage‑to‑orbit super heavy‑lift launch vehicle under development by SpaceX. Musk plans to use the spacecraft to establish permanent bases on the moon and Mars.