Shoppers can also opt for free pick-up at the Click&Go point of the Continente Modelo de Viveiros store in São Roque.
The retailer's delivery service charges start from €6.99.
In August of this year, chief executive Luís Moutinho announced plans to open more outlets in the archipelago and remodel some existing stores with investments worth €7 million.
Pedro Santos, MC's e-commerce director, stated, "We have long believed in this channel (online), and as such, we have invested and will continue to do so to develop and modernise our digital value proposition, which includes a consistent integration with the physical propositions.
"With this arrival in Madeira, more than expanding a service and making life easier for Madeirans, we believe we reaffirm and make clear the importance that this region in growing development has for Continente."
Continente Online was recently recognised as the best online supermarket in Portugal (Best Portuguese online supermarkets 2022 rating) based on customer experience, from the e-grocery rating 2022 Portugal.
In 2021, the retailer redesigned its website and app as it marked its 20th anniversary.
Continente's e-commerce platform, accessible via any device, is equipped with a state-of-the-art navigation system and offers personalised recommendations.
At the checkout, the platform also offers the option to manage substitutions product by product, with alternatives to unavailable items.
Continente Online offers a wide range of products, as well as integration with the Continente loyalty card, same day deliveries, seven days a week, from 8:00 to 23:00, and free Click&Go service in over 150 stores throughout the country.