The accuser had said Spacey bought him alcohol and groped him at a bar on the island of Nantucket, Massachusetts.
The accuser was ordered to take to the stand this month after he said he lost the phone he had used on the night of the alleged assault. Spacey's lawyers had accused the man of deleting text messages and said the phone could be used to prove their client's innocence.
However, he invoked his Fifth Amendment rights against self-incrimination and refused to testify.
In a statement on Wednesday, the Cape and Islands District Attorney's Office said the "unavailability of the complaining witness" had led them to drop the case, reports bbc.com.
The announcement comes after the accuser earlier this month said that he was dropping a civil case against the actor.
The accuser's lawyer, Mitchell Garabedian, said in a statement on Wednesday that his client had "shown an enormous amount of courage under difficult circumstances".
The allegations came after another actor accused a then 26-year-old Spacey of climbing on top of him on a bed when he was just 14.
The actor apologised for any inappropriate conduct, which he said he could not remember.