Amazon.com Inc. is working on plans to roll out its one- and two-hour membership delivery service into Canada later this year, a move that marks a broader push into the country by the Seattle-based retailer, according to people familiar with the matter.

Amazon could begin offering its Prime Now service in Vancouver and Toronto in November and January, respectively, under a pilot program that will deliver groceries and other items within a two-hour window, according to a person familiar with the matter. If the initial launch...