The WestJet flight to Toronto had been leaving the gate at walking speed when it clipped the other plane, also owned by WestJet.
No one was hurt.
The wing tip of the Boeing 737-600 "made brief contact" with the wing tip of the other plane, according to a statement from WestJet.
"There was a shudder — it went through the whole plane," said Steven Staples, who was aboard one of the planes.
"Everybody looked up and out the window and we could see that the tip of the wing of our plane had struck the tip of the wing of another plane in the gate beside us."
'It was a strange feeling'
All 93 passengers aboard the flight to Toronto and all 69 passengers on the flight to Vancouver were asked to return to the airport terminal while crews inspected the planes. They have now been transferred to other flights.
"It was a strange feeling," Staples told CBC News by phone from the airport. "I think everyone was sort of surprised by it. Even the crew said they hadn't really … seen something like that happen before."
The plane heading to Toronto sustained damage, the WestJet statement said.
The plane heading to Vancouver was still being inspected by WestJet later Friday morning, but the aircraft's remaining flights were cancelled for the day.
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