Scotland Yard's Counter-Terrorism Command investigating the Friday attack arrested the 25-year-old from Newport, South Wales this evening.
The Metropolitan Police said that an address in Newport is being searched in this connection.
On Saturday, an 18-year-old man was detained at Dover port, and a 21-year-old was arrested in Hounslow in west London.
Both suspects were being held under the UK's Terrorism Act and being questioned at a south London police station.
The suspects have not been named officially but the 21- year-old has been identified locally as Syrian refugee Yahyah Faroukh.
The latest arrest is also under section 41 of the UK's Terrorism Act, as in the case of the other two suspects.
The arrest was carried out by the Met's Counter-Terrorism Command, supported by Gwent Police and the Welsh Extremism and Counter-Terrorism Unit.
Metropolitan Police Commander Dean Haydon said: "This continues to be a fast-moving investigation. A significant amount of activity has taken place since the attack on Friday. We now have three men in custody and searches are continuing at four addresses."
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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