The 45-year-old man and 52-year-old woman were arrested on Sunday on suspicion of conspiracy to commit arson and have been taken into police custody, the Metropolitan Police said.
It follows an incident at a building in Nelson Street, Whitechapel, in the early hours of Tuesday, which the force said is being investigated alongside a number of apparent attacks on Jewish sites in London since late March.
Met Police said officers were called at 5.16am by the London Fire Brigade to reports of a fire at the former synagogue.
Minor damage had been caused to a set of gates and a lock at the front of the building.
CCTV footage showed the fire had been started deliberately minutes before, officers said.
On Sunday, commander Helen Flanagan, head of Counter Terrorism Policing London, which is leading the investigation, said: “Today’s arrests are a significant step in our investigation into this attack and our inquiries are ongoing.
“Our aim continues to arrest and charge all those responsible for the arson attacks and other incidents targeted at Jewish, Israeli and Iranian sites in recent weeks.
“We will not tolerate these hateful attacks on communities.”
The former synagogue was due to be sold at auction earlier this year. There was a separate bid by a Muslim group to buy the building and convert it into a mosque and community centre.
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