Officers stepped up security in the town center and on public transport and police said one possible target was a night club which was not named. Investigations were continuing but no further details on the nature of the threat were available.
A spokesperson in Offenburg, in the state of Baden-Wuerttemberg and close to the French border, did not give any further details.
Germany is on high alert following deadly extremist attacks in France and Belgium and after a failed asylum seeker from Tunisia drove a truck into a Berlin Christmas market in December, killing 12 people.
On Saturday, police in the city of Essen closed a shopping mall after security services warned of a possible attack.
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