Officers arrested him in the eastern London suburb of Ilford, near Barking, where two of the assailants lived.
The Saturday attack was claimed by the ISIS and follows the May 22 suicide bombing at the Manchester Arena by Salman Abedi, killing 22 people.
There are now two men in custody while another 12 people held following the attack have since been released.
The assailants drove a van into pedestrians on London Bridge, before descending into the nearby Borough Market where they stabbed people out for the night in the bars and restaurants.
Police have identified the attackers as Youssef Zaghba, a 22-year-old Italian national of Moroccan descent, Khuram Shazad Butt, 27, a Pakistan-born Briton, and Rachid Redouane, 30, a self-described Moroccan-Libyan dual national.