Deputy Assistant Police Commissioner Neil Basu says that it's a "significant arrest".
Parsons Green station has re-opened after the attack.
This image shows Parsons Green station in the early hours of the morning following a bomb attack on a packed underground train, in south-west London on September 16, 2017. The police said that the arrest was a "significant" development and that the investigation is advancing well.
"Communities across the United Kingdom can expect to see more officers, both armed and unarmed, on patrol by foot and in vehicles over the weekend".
The suspect, who was not identified, was detained under the Terrorism Act and was being held at a police station in South London, according to the statement.
With the terror threat level at critical, British military personnel may assist police in protection duties at key sites such as Buckingham Palace, government and parliament buildings, as well as at important events across the country.
The Department of Foreign Affairs has confirmed that an Irish person was injured in Tube bomb attack in London yesterday.
Detectives investigating the Parsons Green bombing have arrested a teenager on suspicion of a terror offence, Scotland Yard have said. None of the injuries are thought to be life-threatening.
Authorities are treating the bombing as a terrorist attack.
Police said cordons were put in place around the neighborhood to clear the area for police.
The Islamic State group claimed they were behind the tube incident through its Amaq news agency, though without proof.
"We're chasing down suspects", he told reporters.
Britain's chief counter terrorism officer, Mark Rowley, said last night that this is a very complex police investigation which is continuing at speed.
Prime Minister Theresa May chaired a meeting of the emergency COBRA committee, in the afternoon as Britain's terror threat remained at severe, meaning a terror attack was highly likely.