Unmesh Desai issued a statement via his solicitor criticising bloggers and social media users who leaked that he was under police investigation, in breach of privacy laws.
It was confirmed this week that Mr Desai had been administratively suspended and would sit as an independent at City Hall.
His City and East constituency includes Newham, Tower Hamlets, the City of London and Barking and Dagenham.
“This is subject to an ongoing police investigation and we are unable to comment further at present,” a Labour spokesperson said.
But Mr Desai’s lawyer said the investigation had now ended with his client being cleared of any wrongdoing.
Ali Parker, of Saunders Law, issued a statement on Mr Desai’s behalf.
“Between late December 2024 and today, I was the subject of a police investigation,” it said.
“I have not made any public comment on this until now.
“I cooperated fully with the police investigation. I answered all of the police questions in interview, maintaining my innocence without any legal advice.
“I have today been informed that police are taking no further action in my case. I have always maintained my faith in our system of justice and in the Metropolitan Police.
“I have however been saddened that certain media outlets, political bloggers and users of X (formerly Twitter) have linked my name to this investigation before I was ever charged with any offence.
“Allegations like this spread like wildfire across the internet. In my case, there were very good reasons for pre-charge privacy. It is not right that my name has been tarnished in this way.”
In recent years, a series of legal rulings have effectively changed the law, banning professional media outlets from naming the subjects of criminal investigations unless they have been charged.
Mr Desai, himself a former human rights lawyer, has been an assembly member since 2016 and is a former Newham councillor.
Asked whether he would be challenging his suspension from Labour, he did not respond.
We have contacted the Labour Party to ask whether it will now lift his suspension.
The Metropolitan Police said it would not comment on an arrest unless a media outlet could already tell it the date and location of the arrest, plus the suspected offences.