The 18-year-old was detained on suspicion of preparing a terrorist act, sparking an evacuation of the ferry terminal, Deputy Assistant Commissioner Neil Basu said.
Detectives investigating the bombing were said to be “keeping an open mind” about whether more plotters were involved and Mr Basu said the terror threat would remain at its highest level, indicating another attack was feared.
He added: “Officers from Kent Police had to partially evacuate the port of Dover at around 11.40am this morning and this was to enable them to search the premises as a precautionary measure.
“That work is now complete and they have recovered a number of items during that search.”
A separate search is under way at a house in Sunbury-on-Thames, Surrey - home to foster care couple Penelope and Ronald Jones, who received MBEs for services to children and families.
The surrounding houses were evacuated by counter-terror officers.
The suspect is now being held at a London police station after being arrested by Kent Police.
Mr Basu said: “At this stage we are keeping an open mind over whether more than one person is responsible for the attack and we are still pursuing numerous lines of inquiry and at great pace.”
Echoing the earlier words of Home Secretary Amber Rudd, he added: “All I am prepared to say at the moment is it is a very significant arrest, but as I said we are open-minded.
“If there are other people responsible it’s our job to find them and that is part of the reason that we are remaining at critical threat.”
The Surrey property is registered to Mr and Mrs Jones, 88 and 71, who were honoured by the Queen in 2009.
Several residents said the couple lived there and Nicola Ryder, who lives opposite, described them as “beautiful people”.
She said she knew them just as Penny and Ron, and that they would foster up to seven young people at a time between the ages of 10 and 18.
Long time family friend Serena Barber, 45, said that the Joneses had fostered dozens of children.
She said: “Penny’s a wonderful foster mother. She takes everyone, she doesn’t turn anyone away.”
The couple featured in an interview with Elmbridge CAN, a community group which aims “to build a culture of welcome to refugees” and help settle them in the local community.
The organisation states that Mr and Mrs Jones have been foster parents for almost 40 years and had taken in 268 children - the last eight of which were refugees. It is not clear when the interview was published.
In the interview Mrs Jones said fostering “had its ups and downs”, adding: “They’re all children, it doesn’t matter if they’re sky blue or with pink dots on them - they just need to be loved.”
On the street, residents were rushed from their homes by armed police and are now facing the prospect of not returning before Sunday.
Mother-of-three Mojgan Jamali, among those forced to flee, told the Press Association: “I was in my house with my children and there was a knock at the door from the police.
“They told me to leave. They said: ‘You have one minute to get out of the house and get away.’
“I just got out, I got my three children and we left the house and the street.
Nearby Staines Rugby Club has been opened as a rest centre for evacuees, with an estimated 150 to 200 people already said to have been welcomed through its doors.
Mr Basu said: “Our priorities are to ensure the address in Sunbury is safe, and to identify and locate any other potential suspects.”
He added his team were “quickly and thoroughly searching that address” and “working to ensure it is safe”
Thirty people were injured when the improvised device partially exploded on a District Line train at Parsons Green station during the Friday morning rush hour.
Three victims are still being treated at Chelsea and Westminster hospital, NHS England said.
Earlier the Home Secretary said it was “much too early to say” whether the bomber was part of the current security picture, following comments from US President Donald Trump that the culprit was known to Scotland Yard.
A key strand of the investigation has focused on CCTV as officers comb through footage to establish who planted the device, and when and where it was placed on the train.
The suspect was arrested at around 7.50am, in the port which is the busiest ferry hub in Europe and serves as a commercial gateway to the French coast, including Calais and Dunkirk.
Police have since identified 121 witnesses, of whom 100 have been spoken to, Mr Basu said.
Residents of Cavendish Road in Sunbury-on-Thames were told to make alternative arrangements for Saturday night, although police said the investigation could be concluded by midnight.
Zane Evans, 24, had come with his mother-in-law to help her collect some belongings from inside the cordon.
He said: “She was told that she might be allowed home by midnight but she has decided to stay with friends tonight.
“I think lots of people have decided the same thing.”
On Saturday night, police were escorting residents to their homes so they could pack a bag.