The suspension announced Thursday involves all band performances, including those of the DSU Approaching Storm marching band, the DSU Jazz Ensembles, the concert band and pep bands.
A spokesman said roughly 150 students participate in the bands.
Officials at the historically black institution said the suspension covers the rest of the semester, including the final home football game Nov. 23.
They did not provide details of the alleged hazing but said the university takes such allegations very seriously.
"We need to investigate this, we need to get to the bottom of this, because hazing is not one permitted at Delaware State University. That means we have to stop what's going on with the bands right now in terms of their activities," said university spokesman Carlos Holmes.
The university said the investigation began more than a week ago, and that enough information had been developed to prompt officials to suspend all band activities until the investigation is concluded.