One package arrived at False Creek Elementary School and the other was delivered to St. George's School, The Province reported. One contained what appeared to be a human foot and the other a human hand.
It wasn't known whether the packages, which were opened by staff at the schools, were delivered by the postal service or by courier, the Vancouver newspaper said.
There was no indication whether the packages were a macabre prank or somehow linked to Luka Rocco Magnotta, the 29-year-old Canadian being held in Germany who is wanted in Montreal in a dismemberment case.
Magnotta is suspected in the slaying of 33-year-old Jun Lin, 33, a Concordia University student from China. Parcels containing the victim's hand and a foot were mailed to two political parties in Ottawa.
Prosecutors said Magnotta -- who was arrested Monday at an Internet cafe -- will not fight extradition to Canada.
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Syrian Al Qaida group executes Lebanese soldier