Terms of the deal were not disclosed.
The company began with a pilot project in Waterloo, Ontario, and has been rolling out a network of pick-up stations across the Toronto area.
"We are now excited to share that we have been acquired by Google," BufferBox said in a blog posting.
"We have a huge vision for this space and we couldn't be happier to be building it out within a fantastic organization."
A Google statement said: "We want to remove as much friction as possible from the shopping experience, while helping consumers save time and money, and we think the BufferBox team has a lot of great ideas around how to do that."
The move comes with Google increasingly entering the retail space with its own shopping site and a Google Play Store, which sells not only digital products but hardware such as Google-branded tablets and smartphones.
The service could help Google compete with other online retailers like Amazon, which have similar services.
On Wednesday, Google said it agreed to buy the marketing firm Incentive Targeting in a move that gives the tech giant more tools to work with retailers on discounts and other promotions.