The 28-year-old, whose name was included on the document, said panic alarms have been installed at his home after the address was listed next to a gang name.
Pages from the Met’s Gangs Matrix, which includes the names and suspected gang affiliations of more than 3,000 people, were photographed and circulated on social media.
Watchdog the Information Commissioner’s Office (ICO) is carrying out an investigation into Newham Council over the alleged breach, which was first reported in November.
The man’s lawyer, Victoria Richardson, from Hudgell Solicitors, he and his family say the leak made them feel “exposed” and worrying about their safety.
She said: “The document clearly contained his name and the address of his parents, where they all live together.
“Our client’s name was one of around 150 which was clearly visible, along with other personal details and gang names.
“For our client’s family, it is of course particularly worrying to see their address on this list, knowing it has been shared on social media platforms and not knowing who has seen it, and what the result of that information getting into the wrong hands could be. They feel it has left them and their home exposed.”
The Metropolitan Police has come under fire from human rights groups over its controversial Gang Matrix, and last month watchdog the ICO concluded it had committed multiple and serious breaches of data protection laws.
Force bosses said they already have an action plan to bring the database in line with the law and will continue using the Gang Matrix to reduce the impact of gang violence.
Information on the database is shared with agencies such as social services, housing authorities and education staff.
Mrs Richardson added: “Whatever agreements or policies were in place, if any, they were clearly not enough and it is quite shocking that such a sensitive document could end up on social media.
“It is obviously a clear and serious breach of data protection laws but also effectively means that some of the most sensitive police intelligence was leaked onto a platform where it can be widely spread in a matter of minutes. It is beyond belief.”