Almost a week after the theft from the site north-west of Munich, Bavarian police said they would offer the money for information which helped clear up the mystery.
The gate was stolen on Saturday night into Sunday morning.
The thieves apparently timed their intrusion between the rounds of the security guards watching the former camp, which has no surveillance system.
Police said earlier this week they were chasing leads and suspected a neo-Nazi motive but no arrests have been made yet.
Dachau's partner town of Fondi in Italy has offered to replace the iron gate.
Germany's Jewish population has reacted with anger to the pillaging of the gate
Around 200,000 people were imprisoned at the camp between 1933 and 1945, tens of thousands of them dying of overwork, undernourishment, medical experiments, torture and violence.
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