Scotland Yard's Counter-Terrorism Command investigating the Friday attack claimed by the Islamic State group arrested the 21-year-old from Hounslow in west London late last night.
An 18-year-old man was arrested in the port area of Dover yesterday. None of the suspects have been named by the police.
Both suspects were being held under the UK's Terrorism Act and being questioned at a south London police station.
"What it indicates is that good progress has been made," she said.
Rudd earlier today told the BBC that the second arrest suggests the attacker was not "a lone wolf". "But as this unfolds and as we do our investigations, we will make sure we find out how he was radicalised if we can," she said.
The minister alsodenied US President Donald Trump had received any leaked security information when he tweeted about the terror attack.
Rudd added her voice to British Prime Minister Theresa May's rebuke to Trump on the matter: "It's never helpful to have speculation about an ongoing operation, and I would include the President of the United States in that comment.
"It is pure speculation, absolutely."
She added that 24 million pounds of new government money was going to counter-terrorism operations across the country.
Thirty people were injured during the attack in which an improvised explosive device was detonated on a Tube train at Parsons Green underground station during morning rush hour.
Basu said in a statement his department was "still pursuing numerous lines of enquiry and at a great pace."
Met Police counter-terrorism specialist firearms officers yesterday evacuated buildings as they began searches at a residential address in Sunbury, Surrey, southeast England.
The search remains ongoing as it emerged that the home belongs to an elderly British couple honoured with an Member of the Order of the British Empire (MBE) medal by Queen Elizabeth II in 2010 for their efforts at fostering hundreds of refugee children.
The Islamic State group has said it was behind the bombing but Met Police's Assistant Commissioner Mark Rowley said it was "very routine" for IS to claim the attack, whether in contact with those involved or not.
The explosion, described as a "bucket bomb", sent a "fireball" through the Tube causing burn injuries to several commuters.
The main device, which had been fitted with a crude timer using shop-bought fairy lights, failed to detonate, meaning hundreds of people were spared death and serious injury.
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