The young man was arrested in the early hours of Thursday in Thornton Heath, south London. The other arrests had taken place in Dover on the south coast of England, Hounslow in west London and Newport in Wales.
A homemade bomb went off on September 15 during the morning rush hour on a packed underground Tube train at Parsons Green station, sending flames through the carriage, although it appeared that the device did not fully explode.
It was the fifth major terrorism incident in Britain this year.
“This continues to be a fast-moving investigation. A significant amount of activity has taken place since the attack on Friday,” said Commander Dean Haydon, head of the Metropolitan Police’s Counter Terrorism Command.
“We now have six males in custody and searches are continuing at five addresses. Detectives are carrying out extensive inquiries to determine the full facts behind the attack,” he said.
The other men in custody in a south London police station are an 18-year-old, a 21-year-old, a 25-year-old, a 30-year-old and a 48-year-old.