"Priory Alley") is a street in the Old Town of Copenhagen, Denmark.

It runs from the site where Amagertorv turns into Vimmelskaftet on the pedestrianized shopping street Strøget in the south to Skindergade in the north.

A short street links Klosterstræde to the square Gråbrødretorv to the east.

It was the most important Franciscan priory in Denmark but was destroyed during the Reformation.

The building at the corner with Amagertorv was built for Kjøbenhavns Laane- og Discontobank in 1906 to design by Axel Berg.