  Neutrinos with large self-interactions, arising from exchange of light
scalars or vectors with mass $M_\phi\simeq 10{\rm MeV}$, can play a useful role
in cosmology for structure formation and solving the Hubble tension. It has
been proposed that large self-interactions of neutrinos may change the observed
properties of supernova like the neutrino luminosity or the duration of the
neutrino burst. In this paper, we study the gravitational wave memory signal
arising from supernova neutrinos. Our results reveal that memory signal for
self-interacting neutrinos are weaker than free-streaming neutrinos in the high
frequency range. Implications for detecting and differentiating between such
signals for planned space-borne detectors, DECIGO and BBO, are also discussed.
