The constitutional court in Karlsruhe found in favour of a man who was given a life sentence for killing two people on a yacht in 1982.
The man, who was released from prison in 2002, is now fighting to distance his family name from reports about the case.
The decision could mean publications are forced to restrict search engine access to their online archives in such cases.
His full name still appears in online searches as part of an archived article in German weekly Der Spiegel. His case was initially rejected by a federal court in 2012 on the basis that his right to privacy did not outweigh public interest and press freedom.
But Germany's highest court has now thrown out that initial ruling, meaning his case will now return to the federal courts.
Yet the court also insisted that individuals could not unilaterally claim a right to be forgotten and that its decision had been influenced by the amount of time that had passed since the crime.
READ ALSO: 60,000 Germans want Google to forget them
Longstanding legal dispute
The “right to be forgotten” has been the subject of a longstanding legal dispute involving Google and the EU.
In 2014, a European Court of Justice ruling forced search engines to comply with requests to remove results.
Google hit back last September when the same court ruled that the right to be forgotten only applied to search results in Europe.
In a separate case, the German constitutional court ruled against a woman campaigning to have the transcript of a TV programme from 2010 removed from searches of her name.
In the TV show, the woman had been accused of treating employees unfairly.
The court described her complaint as “unfounded”.