A 17-year-old boy and a 19-year-old man were taken into custody in connection with the incident, which occurred early on Sunday morning, police said on Monday.
The fire caused minor smoke damage to an internal room and no injuries were reported.
The attack on Kenton United Synagogue was the latest in a series of arson incidents targeting Jewish sites across the capital in recent weeks.
On Friday night, police said there was an attempted arson attack on a business premises linked to the Jewish community.
Two suspects were arrested earlier in April over an attempted arson attack at another synagogue in the capital.
In March, several ambulances belonging to the Jewish volunteer emergency service Hatzola were set alight while parked near a synagogue in the Golders Green area of north London.
Police also briefly cordoned off an area near the Israeli embassy in London at the weekend following an online report that it had been targeted with drones carrying "dangerous substances".
Officers later said items recovered did not contain any harmful or hazardous materials.
Attacks on Jewish people and Jewish targets have risen in Britain since the October 2023 Hamas assault on Israel that triggered the war in Gaza, according to police and community groups.
British security officials have previously warned that Iran has sought to use criminal proxies to carry out hostile activity in the UK.
A pro-Iranian government group, which says it is also behind a spate of attacks across Europe on US, Israeli and Jewish targets, has said it was responsible for the Kenton attack.
"As the conflict in the Middle East continues to evolve, counter-terrorism policing and our partners remain alive to the threat of Iranian hostile activity in the UK," Vicki Evans, senior national co-ordinator for Counter Terrorism Policing, told reporters.
"We are aware of public reporting that suggests this group may have links to Iran. As you would expect, we will continue to explore that question as our investigation evolves."
Chief Rabbi Ephraim Mirvis said the Kenton fire, which did not cause any significant damage, was the third "cowardly" attack on Jewish sites in the UK capital in less than a week.
"A sustained campaign of violence and intimidation against the Jewish community of the UK is gathering momentum," Mirvis said on X.
"Thank God, no lives have been lost, but we cannot, and must not, wait for that to change before we understand just how dangerous this moment is for all of our society."
