Metropolitan Police Deputy Assistant Commissioner Neil Basu said that the arrest was "significant".
Basu stressed that the arrest would be followed by further actions by the police, providing no additional details on the issue.
The UK has witnessed a series of attacks this year, with the bombing of a concert in Manchester in May, a stabbing spree around the London Bridge area in June and a March attack in which a man drove a vehicle into crowds on Westminster Bridge.
Twenty-nine people are in hospital, most of whom suffered "flash burns", after the improvised explosive device went off at Parsons Green station in south-west London at around 8.20am.
As of Saturday morning, officials were not sure whether more than one person had been involved in the bombing that - according to a new police report - left 30 people injured.
But it remained unclear on Saturday if they believe there is another suspect at large, and police urged people to remain "calm but alert".
The attack saw 29 people hospitalised many with burns
The Daesh terror group (banned in Russia) reportedly claimed responsibility for the blast.
Shiraz Maher, an expert on radicalisation at Kings College London, said it was unusual for such claims to be made while the suspect was still at large.
The British police added that "This arrest would lead to more activity from our officers".
Prime Ministerka the UK Theresa may on Friday evening, September 15, said that after the terrorist attack in London, the terrorist threat level in the country increased from "serious" to "critical".
Announcing the change in the United Kingdom threat level, Prime Minister Theresa May said the military would be providing support to police and would replace officers on guard duty at national infrastructure sites that are not accessible to the public.
Britain's terror threat level has been raised from Severe to Critical, meaning another attack may be imminent, in the wake of the Parsons Green train blast.
Arsene Wenger: Arsenal can use Liverpool loss as motivation at Chelsea
Arsenal hope that by keeping Sanchez at Emirates Stadium, they will be the ones to benefit from his undoubted ability this season. Alexis Sanchez may have wanted out of the club over the summer, but Arsene Wenger says the forward is "happy" at Arsenal .