We show that a negative relative demand shock in a sector with downwardly rigid prices, like the service sector, can generate substantial inflation. Such a shock induces an equilibrium decline in the relative price of services. If price adjustment costs are non-existent or symmetric, then this takes place through a simultaneous decline in services prices and increase in goods prices, resulting in, on net, little inflation. If prices in the services sector are downwardly rigid, however, this takes place mostly through an increase in goods prices, resulting in inflation. To illustrate the relevance of this mechanism in practice we provide evidence on the downward rigidity of person-to-person service prices during the Covid pandemic of 2020-2021. We then introduce downward price rigidities in a multisector New-Keynesian model and show how they can result in inflationary relative demand shocks.