A statement from the bid team said financial reasons and a global fall in oil prices were behind the withdrawal.
The Games, which were held in Glasgow last year, were staged in Edmonton in 1978 and the city has said they will bid again to host the 2026 event.
"This hasn't been an easy decision," said bid chairman Reg Milley.
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"Our team has been working tirelessly these last months to put together an extraordinary bid.
"But at this time it would not be right to move forward with our bid when cuts are being made in our communities to programmes like education and health."
An Edmonton bid for the 2026 Games could be up against a bid from Wales.
Cardiff City Council and the Welsh government are conducting a feasibility study on whether to table a bid for the event.
Australia's Gold Coast will host the Games in 2018, and Durban is set to be named as the 2022 host when the official announcement is made on 2 September, 2015.
David Grevemberg, chief executive of the Commonwealth Games Federation, said: "We're obviously disappointed to hear Edmonton will not be part of the host city bidding process for the 2022 Commonwealth Games.
"We now look forward enthusiastically to working with the Durban 2022 bid team and their partners through the evaluation process so we can realise the ambitions of delivering Africa's first Commonwealth Games.
"I'm confident there will be a great 2022 Commonwealth Games to follow on from the fantastic experience of Glasgow and the dynamic Games currently shaping up in the Gold Coast for 2018."
Canadian city Edmonton has withdrawn its bid to host the 2022 Commonwealth Games, leaving Durban in South Africa as the only remaining bidder.