A man was arrested in March and was cautioned by police, but he is not the man in custody for Thursday’s attack, a statement from London’s Metropolitan Police said.
Witnesses said Cox, a 41-year-old with two children aged three and five, was repeatedly shot and stabbed in Thursday’s assault in the Yorkshire village of Birstall.
Her murder came one week before Britain holds a referendum on whether to stay in or leave the European Union, a vote which has sparked a divisive and bitter campaign.
“Officers received an allegation of malicious communications from Jo Cox MP, and in March 2016 arrested a man in connection with the investigation,” the police statement said.
“The man subsequently accepted a police caution. The man who accepted the police caution is not the man in custody in West Yorkshire.”
The Times newspaper reported that police were considering putting in place additional security for Cox when she died.
A 52-year-old man, named by British media as Thomas Mair, was arrested shortly after Cox was attacked.
Neighbours told newspapers that he was a loner who had lived in the area for decades, but there were indications he had extreme right-wing leanings.