The fish were each wrapped in black cloth and had several spices accompanying them.
Police said the items appeared to be left behind as a part of a ritual in Santeria, a traditionalist African-Caribbean faith.
Lt. Tom Cleary said the fish were discovered Saturday in the open grave at St. Joseph's Cemetery on Truman Avenue.
"We think it might be one of these types of Santeria rituals, but we're not sure," Cleary told The Post.
He did not say if the person who was to be buried in the grave had any connection to the fish.
He said investigators don't believe the fish are connected to a macabre offering left at St. John's Cemetery, on Saw Mill River Road, on March 14.
In that incident, a large animal heart riddled with pins, a rubber rooster wrapped in a bandanna and a photograph of a smiling man dressed in a suit were left at the grave of Robert Newton Flagg, who died in 1897.
About six headstones were toppled and adorned with candles.
"That was more of a criminal mischief type of thing," Cleary said.
A worker at St. Joseph's said offerings were common in the cemetery.
"We sometimes have Santeria and we have some voodoo. Other times, we don't know what it is," the worker said.
The fish could have been left as an offering to "Yemaya," the goddess of the ocean in Santeria, an expert said yesterday.
Dr. Miguel De La Torre, a professor at the Iliff School of Theology in Denver, who wrote "Santeria: The Beliefs and Rituals of a Growing Religion in America," said that an offering to Yemaya would not be done to put a curse on somebody.
"She's a cosmic mother figure," De La Torre said. "She's not the sort of person you would invoke to do damage to somebody."
He said Yemaya's special day was Saturday and fish are usually sacrificed in her name.
But he said whoever left the fish at the cemetery appeared to be confused because normally, burial grounds would be the site of an offering to Oya, the goddess of death.
"Either the person doesn't know or understand it," De La Torre said. "There seems to be a bit of confusion here."