Museum officials told The Seattle Times that the statue was covered with white paint or a similar substance on Thursday.
The damage is being assessed and the statue will be restored, museum officials said.
“We are deeply pained by this act targeting the memory of a beloved artist in Seattle and around the world,” museum officials said in a statement.
Cornell was a leader of the grunge movement with Seattle-based Soundgarden group that won critical and commercial acclaim.
Cornell killed himself in 2017 following a performance in Detroit. He was 52.
The statue was commissioned by his wife, Vicky Cornell, and unveiled in 2018. It shows the singer performing with his Gibson guitar.
In an Instagram post, Vicky Cornell wrote that she and her children were “heartbroken” by the vandalism.
“The statue is not only art, but a tribute to Chris, his incomparable musical legacy and everything that he stood for.”