The retailer is offering dishes such as stews, sushi and sandwiches to order from two Tottenham Court Road sites.
Customers can request delivery from breakfast to early evening Monday to Friday.
Supper launched in 2015 as a high-end restaurant delivery service, targeting fine dining and Michelin-starred restaurants.
It secured a £300,000 investment from the owners of the Barworks group in 2017, and now works with restaurants including Jean Georges at The Connaught, Cinnamon Kitchen, Homeslice and Farzi Café.
“Supper is going from strength to strength with quarterly revenue growth throughout 2019 and 2020 forecast to continue that trend, and delivering from great retailers like Planet Organic is a key part of this,” says Supper founder and CEO Peter Georgiou.
Planet Organic is not the first supermarket to enter the meal delivery market. Last year Sainsbury’s teamed up with Deliveroo for a two-month trial to test home-delivery of hot pizzas made in its stores.