Target Corp has partnered with Instacart to deliver groceries for just $3.99 per order, as it overhauls its food business and competes with Amazon.com's grocery delivery service. The discount retailer will launch a pilot to test the offering in its hometown of Minneapolis and customers in some areas will be able to order online for food, pet products and baby items from two Target stores and have them delivered to their homes.

The push expands online order options for Target customers, who can get free delivery within five days on a $25 minimum order.

At $3.99 per order, Target customers would have to place 75 orders to match the cost of Amazon's annual $299 delivery fee for groceries.