The museum had previously exhibited a portrait of Trump with a caption noting that he had been impeached twice.
The singer crawls and leaps through an installation that looks like Walter De Maria's New York Earth Room.
The sale includes items such as his personal print of Eraserhead.
Diane Prince previously said the 1995 piece was "just a protest work suitable for display."
Aoki’s anamorphic terracotta sculpture stood out for its “honest expression of the ancestral coil process, the jury said in a statement.