The Burlington Police Department tweeted a photo of the undelivered packages, saying a "diligent grounds keeper" at Chestnut Hill Cemetery northwest of Boston came across something "suspicious" in a trash receptacle and alerted authorities.
The packages were addressed to Burlington residents, so the officers notified Amazon and began delivering them.
Police did not say how many were found, but WFXT-TV reported officials said there were about 40.
Burlington Police Officer Roberto Reyes told the station the packages were dated Sept. 22, meaning they should have been delivered Sunday.
"The few residents I did speak to today, a lot of people weren’t home today, unfortunately, but the few residents I did speak to today were surprised to see me obviously, but once they were explained the circumstances, they were very gracious," Reyes said.
Authorities are investigating how the packages ended up in the cemetery. The person responsible could face criminal charges, they said.