The Martha's Vineyard Times reported Elliot Blume-Pickle was arrested Tuesday and charged with rape by force and assault and battery for the alleged June 25 assault of a teen female at his family's Martha's Vineyard estate.
Tisbury police described the alleged incident as "acquaintance rape" when talking to the newspaper.
Blume-Pickle pleaded not guilty to the charges and posted $5,000 bail, the Times said.
The New York Post identified Blume-Pickle as the famous author's grandson and said a representative for Blume's publishers declined to comment on the case Thursday night.
Blume, 62, is the author of such young-adult classics as "Are You There God? It's Me, Margaret?," "Deenie," "Blubber," "It's Not the End of the World" and "Then Again, Maybe I Won't."