"Its material value is small but the spiritual loss is much greater," the cathedral's provost, Gerd Bachner, was quoted in the police statement from yesterday as saying.
Bachner urged the thieves to "come to their senses" and return the relic.
A visitor to cathedral noticed early yesterday that the cloth was missing from its glass case, which was built to recall a visit by the pontiff to Cologne in November 1980.
Police released a picture of the glass with a hole smashed by the thieves.