A "classic" service will cost $179 for five meals for a family of four, while the "gourmet" service for two people costs $139 for four meals.
There is no delivery charge.
Despite a tough economic climate Gattung said she thought there would be enough consumers willing to shell out on the service.
"We've worked really hard on getting a model that we think will work, but it's early days."
My Food Bag is the brainchild of Auckland entrepreneur Cecilia Robinson, who saw a similar business on a visit to her native Sweden.
Mike Wales, formerly of grocery store operator Nosh, is the firm's general manager.
Gattung, who was one of New Zealand's highest paid executives while with Telecom, didn't want to reveal the size of her stake or how much she had invested, saying that information was "confidential".
But the Companies Office website says Gattung and Wellington lawyer Margaret Doucas own 40 per cent of My Food Bag, while Lim and partner Carlos Bagrie hold a 20 per cent stake.
The remaining 40 per cent is owned by Robinson, her husband James and a company linked to Auckland law firm Gellert Ivanson.
Wellington-based Gattung said My Food Bag was her main business venture at the moment, although she had made some other investments.