The man was arrested at an address in Ilford, east London
The 30-year-old was arrested in the early hours of Wednesday morning at an address in Ilford, east London.
The arrest comes after the three extremist killed seven people after they drove a van through pedestrians on London Bridge before getting out of the vehicle and launching a knife attack in Borough Market.
Pakistani-born Khuram Butt, Moroccan-Italian Youssef Zaghba, 22, and Moroccan-born Rachid Redouane, 30, were shot and killed by armed police just eight minutes after the first call to emergency services.
A Metropolitan Police spokesman said: "Detectives investigating the London Bridge terror attack have carried out a search warrant at an address in east London in the early hours of Wednesday June 7.
"Officers from the Met's Counter Terrorism Command, supported by officers from the Territorial Support Group, entered the address in Ilford at around 1.30am.
"A 30-year-old man was arrested on suspicion of the commission, preparation or instigation of terrorist acts (contrary to section 5 Terrorism Act 2006) and has been taken into custody at a south London police station under the Terrorism Act 2000.
"A search of the address is ongoing."