During the coronavirus disease‐2019 pandemic, online grocery shopping experienced a never seen popularity in many countries. To study how the globally active online grocer Amazon Fresh reacted to this extraordinary demand increase, we analyzed a large dataset of daily Price quotes for over 19,000 products for the customer location, Los Angeles. We found that contrary to the US consumer food price index, the overall price level at Amazon Fresh did not increase during the pandemic, but even slightly decreased for several product groups. Amazon seems to follow its low‐price strategy also in the grocery sector, even in times of high demand. However, during the lockdown phase, there were more price increases for certain highly demanded product groups such as frozen and prepared foods. Moreover, fewer prices were communicated as promotional prices. Because this change did not influence the general price level, we conclude that such promotional prices are used more as a marketing tool than as a price‐setting instrument.