The 19-year-old was held in Barking on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.
Police said six other suspects remain in custody and searches are ongoing.
Eight people were killed when three men drove at pedestrians on the bridge and stabbed people in Borough Market.
The man arrested on Sunday is being held at a police station in south London.
The six men still in custody, all aged between 27 and 30, were also arrested in east London - four in Ilford, one in Newham and one in Barking.
Thirteen people arrested as part of the investigation have been released without charge, while a 33-year-old man held in Ilford on 8 June has been bailed.
Over the weekend, police released images of fake explosive belts worn by the three attackers, named as Khuram Butt, Rachid Redouane and Youssef Zaghba.
Borough Market is hoping to re-open "later this week", managing director Darren Henaghan has said.
Traders were officially given access to the market on Monday - for the first time since the terror attack - to allow them to start clearing up and prepare to resume business.
On Saturday night, bars and restaurants across the capital donated money to a British Red Cross UK fund for victims of terror attacks and their families, as Londoners were encouraged to show "unity and resilience" a week after the attack.
The fund has raised more than Â£700,000 since it started on 4 June.
And on Sunday, Southwark Cathedral - which had been cordoned off in the days after the attack - re-opened its doors for the first time.
Another man has been arrested in connection with the 3 June terror attack on London Bridge, bringing the total number of arrests to 21.