The packages contained a human hand and foot, Canadian police said.
Canadian police declined to confirm whether the incident was linked to suspect Luka Rocco Magnotta.
Luka Rocco Magnotta, 29, on Tuesday appeared in a Berlin court – a day after he was arrested at an internet cafe.
The Canadian authorities are now preparing papers to request his extradition, and Luka Rocco Magnotta has reportedly said he will not fight the move.
Luka Rocco Magnotta is suspected of killing Chinese student Jun Lin, 33, in Montreal, and posting severed body parts to political parties in Canada.
Jun Lin’s relatives have now arrived in Montreal and are expected to meet police shortly.
On Tuesday, Canadian police said a package with what appeared to be a human hand was opened at Vancouver’s False Creek Elementary School.
Another parcel with what looked like a human foot was found at St George’s school for boys in the western Canadian city.
“There is no indication any student or staff has been targeted at any school,” Vancouver Deputy Police Chief Warren Lemcke told a news conference.
He added that “this must have been a very traumatic incident” for pupils and teaching staff at the schools.
Jun Lin’s hand and foot were discovered last week after they were mailed to Canada’s political parties.
Police say Jun Lin’s other hand, foot and head are still missing.
Police say Luka Rocco Magnotta flew from Montreal to Paris on 26 May, eventually travelling by coach from France to Germany.
Montreal Police Commander Ian Lafreniere said investigators were extremely relieved and pleased about the arrest.
“We said from the beginning that the web has been used to glorify himself and we believe the web brought him down,” he added.
“He was recognized because his photo was everywhere.”
Luka Rocco Magnotta was picked up in the cybercafe in Berlin’s Neukoelln district, where he had reportedly been reading articles about himself.
“A colleague recognized him from his photo because he’d just read the newspaper,” the cafe owner told the Associated Press news agency.
The employee, Kadir Anlayisli, ran outside and flagged down a passing police van.
Police said there had been no struggle when Luka Rocco Magnotta was arrested on Monday.
Confronted by seven police officers, Luka Rocco Magnotta “tried at first giving fake names”, police spokesman Guido Busch said.
“But in the end he just said: <<You got me>>.”
The suspect had reportedly worked as a bisexual porn actor and model.
Jun Lin, who was from Wuhan in China, had been enrolled as an undergraduate to study engineering and computer science at Concordia University in Montreal.
Investigators say a video posted online, in which a man apparently uses an ice pick to kill another man, is believed to show Jun Lin’s murder.
Luka Rocco Magnotta faces charges in Canada of murder and threatening Canadian politicians.
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