We have performed three searches for high-frequency signals in the solar neutrino flux measured by the Sudbury Neutrino Observatory, motivated by the possibility that solar g-mode oscillations could affect the production or propagation of solar 8B neutrinos. The first search looked for any significant peak in the frequency range 1-144 day–1, with a sensitivity to sinusoidal signals with amplitudes of 12% or greater. The second search focused on regions in which g-mode signals have been claimed by experiments aboard the Solar and Heliospheric Observatory satellite, and was sensitive to signals with amplitudes of 10% or greater. The third search looked for extra power across the entire frequency band. No statistically significant signal was detected in any of the three searches.