Local customers who have shopped through the retailer's online groceries website will be eligible for the service.
The trial will test whether electric cargo bikes could be a more efficient way of getting groceries to customers living in busy cities.
Bikes will be able to use cycle lanes to avoid traffic during peak delivery hours, and park closer to customers' homes than is often possible for traditional delivery vans.
They will also be beneficial to the environment, producing zero emissions and no noise pollution.
Clodagh Moriarty, Director of Online at Sainsbury’s, said: “We’re delighted to be the first supermarket to trial grocery deliveries by electric cargo bikes.
"We’re always looking for new ways to make sure we can best serve our customers and this trial will help us explore whether there might be a more flexible way to deliver Sainsbury’s groceries to those who live in busy cities.”
If successful, the trial may be rolled out to other areas across the UK.
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