Kent Police detained the 18-year-old man in the port area of Dover on Saturday morning.
The suspect will be moved to a south London police station, the Metropolitan Police said.
Deputy Assistant Commissioner Neil Basu said: "We have made a significant arrest in our investigation this morning. Although we are pleased with the progress made, this investigation continues and the threat level remains at critical.
"The public should remain vigilant as our staff, officers and partners continue to work through this complex investigation. We are not, at this time, changing our protective security measures and the steps taken to free up extra armed officers remain in place.
"This arrest will lead to more activity from our officers. For strong investigative reasons we will not give any more details on the man we arrested at this stage."
The Met said 45 witnesses have been spoken to and 77 images and videos have been sent to detectives by members of the public.
A renewed appeal for information was put out by the force, asking anyone with information to call the Anti-Terrorist Hotline on 0800 789 321 or 999 in an emergency.
An improvised device detonated on a packed District Line train at Parsons Green station during the Friday morning rush hour, injuring 30.
NHS England said 19 victims were taken to hospital by ambulance, while 11 had presented themselves.
Three still remain in hospital care, the health service said.
A huge manhunt was launched for the potential network of terror plotters behind the attack as the country was braced for further attempts.
The country’s top counter-terrorism officer suggested on Friday night that more than one suspect could have been involved in the attempt to slaughter commuters in a tube carriage.
Assistant Commissioner Mark Rowley said police were “chasing down suspects”, while suggestions were made by Donald Trump that the bomber was known to Scotland Yard.
The device reportedly contained the explosive triacetone triperoxide (TATP) and nails, but is thought to have only partially detonated from inside a bucket.
Parsons Green station was re-opened in the early hours of Saturday, shortly after the Prime Minister announced that the Joint Terrorism Analysis Centre had set the terror threat at its highest level.
It was the second time this year the country was placed at “critical”, meaning an attack “may be imminent”, Theresa May said - the other occasion being the Manchester Arena bombing which killed 22 people in May.
It came after Scotland Yard and the Prime Minister rebuked the US president over his claim the Parsons Green Tube bomber was “in the sights” of detectives.
There were fears the number of those hurt could have been much higher - with the real potential for life-threatening injuries - had the bomb, which was concealed within a supermarket carrier bag, fully exploded.
It is not yet known whether the bomb, which was reportedly fixed with a timer, went off at its intended target.
The train - bound for Edgware Road - was just pulling into the station in south-west London when the device exploded, in the rear carriage, sending passengers fleeing to safety.
Numerous commercial ferries travel from Dover bound for Dunkirk and Calais in France each day.