The 29-year-old was held during a raid at a residential address in Newham, east London, in the early hours of Friday, Scotland Yard said.
The arrest brings to four the number of men held in connection with Saturday’s attack, in which eight people died.
As the number of arrests mounted it emerged the Saudi Arabian Football Federation had apologised “unreservedly” after its players snubbed a minute’s silence for the victims.
The Saudi squad seemingly declined to line up and pay their respects with the Australian team during a World Cup qualifier, with one seen bending to tie his shoe lace.
In a statement the federation said it “deeply regrets and unreservedly apologises for any offence caused”.
It added: “The players did not intend any disrespect to the memories of the victims or to cause upset to their families, friends or any individual affected by the atrocity.
“The Saudi Arabian Football Federation condemns all acts of terrorism and extremism and extends its sincerest condolences to the families of all the victims.”
A British Transport Police officer stabbed in the eye during the attack described his anguish at not being able to do more to help those killed and injured.
The officer, who has not been named, said in a statement: “I feel like I did what any other person would have done. I want to say sorry to the families that lost their loved ones.
“I’m so sorry I couldn’t do more and I want you to know I did everything I could.”
The man arrested yesterday was taken to a south London police station while officers from the Metropolitan Police’s Counter Terrorism Command searched the property.
A total of 17 people have now been arrested as part of the investigation. Twelve people held in the initial stages of the probe were released without charge earlier this week, while a man arrested in Ilford on Wednesday has been bailed.
A more in-depth profile of the perpetrators has continued to build up as the investigation spreads, including the role online material played in radicalising the attackers.
Relatives of 27-year-old Khuram Butt said he drew inspiration from extremist videos on YouTube and wanted to fight in Syria but had his passport taken away by family.
Fahad Khan, 36, the cousin of Butt’s wife Zahrah Rehman, claimed his younger relative watched the hateful tirades of preachers online and supported the Islamic State terror group.
He said: “Khuram, I know he was inspired by one of the sheikhs who was giving lectures on YouTube, and he belonged to one specific sector of Islam which had very rigid and strict views.
“Videos about fighting non-Muslims for no reasons, innocent non-Muslims. He wanted to go to Syria, yes. I heard from (an) uncle that he wanted to go to Syria to fight, but because of the family pressure, or it might be the intervention by the authorities who seized his passport or whatever, he couldn’t go there.”
The internet was also described as a catalyst in the radicalisation of Butt’s co-conspirator Youssef Zaghba, 21, whose mother claimed: “He had the internet and from there he got everything.”