The Grand Rapids Press reports the coupon must be used Friday or Saturday and is good as long as shoppers spend $50.
The coupon is accompanied by a message saying: "You deserve better. We're committed to offering our customers a great experience, and that didn't happen during a network outage."
Grand Rapids-based Meijer Inc. has stores in Michigan, Illinois, Indiana, Ohio, and Kentucky.
The outages lasted about 30 minutes and happened on Feb. 27-28, forcing some shoppers to leave their carts behind if they didn't have cash. Meijer spokesman Frank Guglielmi says a glitch at the company's point-of-sale system caused an outage throughout its stores.