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.

Caitlin Ruddy had been with a group of teenagers on the north pier at Cullercoats Bay on Saturday evening.
Northumbria Police said she was rescued from the side of the bay by a member of the public.
Caitlin died in hospital after suffering a cardiac arrest. Her mother, Sabrina Cook, said she had lost her "everything".
Mrs Cook has warned young people "not to take water for granted, because it is dangerous".
"I've lost my daughter through it," she said.
"She was stunning, she was my everything really, she was my friend."
Caitlin's friends and family have been paying their respects at Cullercoats Bay, writing messages in the sand and leaving flowers.
A RNLI lifeboat, a Coastguard search-and-rescue helicopter and police were called to the scene at about 20:00 GMT.
Caitlin was taken to Northumbria Specialist Emergency Care Hospital in Cramlington.
Another 15-year old girl, and a boy and girl both aged 14, were also taken to hospital as a precaution but were uninjured, police said.
Ch Insp Paul Knox issued a warning that "people can be taken unawares by the strength of the waves" when it is dark and cold.
"People should always be careful around water and if the sea is looking rough with waves pounding on to the pier, we would advise people to be particularly cautious and keep their distance," he said.
A Cullercoats resident who witnessed the rescue operation said the weather had been "absolutely freezing".
Newcastle University lecturer Clare Guilding said the beach was a popular place for teenagers to congregate.
"It was minus 2C, but once you get out on the front it was just bitterly, bitterly cold," she said.
Another man has been arrested in connection with the 3 June terror attack on London Bridge, bringing the total number of arrests to 21.
[NEXT_CONCEPT]
A 15-year-old girl has died despite being rescued after she was swept into the sea in North Tyneside.