"The rate of adoption over the last 12 to 18 months -- I think it's growing faster than anybody expected," Birmingham said. "It is the fastest-growing part of our business."
Grand Rapids, Mich.-based Meijer says its online food business has grown rapidly.
The company said it is on pace to make more than a million deliveries made from its stores by year-end.
Online service also can help smaller grocery operators grow.
"We look at it as a way of expanding our trade area without having to build more stores," said Darlene Murphy, director of marketing for Metcalfe's Market, which has three stores.
Food producers also are watching the situation closely.
Hamdi Ulukaya, CEO and founder of Chobani yogurt, sees it as a kind of throwback, especially for products like his company's.
"I see the milkman coming back, I really do, for fresh food," Ulukaya said. "You wake up and go to the door and there's your milk and cheese. It's coming back to what it was in the early days."
Digital grocery shopping essentially has been a phenomenon waiting to happen, with the industry finally catching up to the demands of younger consumers, said Jim Hertel, senior vice president of Willard Bishop, a Chicago-area food retail and production consultancy that is part of Inmar Analytics.
"Millennials are just online all the time," Hertel said. "Now that they are forming households, it's less about their adopting online and it's more that they are shopping for food and doing it the way they would normally do anything, which is online."