Judges in the western city of Cologne sided with environmental campaign group Deutsche Umwelthilfe, which filed the case.
The group, whose carriers include Lufthansa, Eurowings, Austrian, Swiss and Brussels Airlines, said it was studying the judgement, which can still be appealed.
The adverts say that emissions can be "compensated" for by financial contributions to projects that would "either reduce carbon emissions in the future or remove them from the atmosphere".
But Lufthansa had not demonstrated how this was the case and falsely gave the impression that a payment could make a flight carbon-neutral, the court said, ordering the group to stop making the claim.
The head of Deutsche Umwelthilfe, Juergen Resch, said the ruling was one "of the clearest and hence most important" to date when it came to "false advertising and greenwashing".
It is not the first time Lufthansa's environmental claims have failed to fly.
In December 2023, Britain's advertising regulator ordered the German airline to remove references to flying "more sustainably" in adverts, also telling Air France and Etihad to stop making similar claims.
The Lufthansa group says it aims to halve its net carbon emissions by 2030 compared to 2019 and to go carbon neutral by 2050, though the aviation sector is among the toughest to decarbonise.
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