Officers shot and killed the suspect, Greater Manchester Police said.
But it took authorities some time to confirm he was dead because of concerns that he had an explosive.
The Metropolitan Police in London, who lead counter-terrorism policing operations, declared the assault a terrorist attack.
Assistant Commissioner Laurence Taylor said two other suspects were arrested, but he provided no further information on the arrests.
He said police believe they know the identity of the suspect, but have not confirmed it.
The attack took place as people gathered at an Orthodox synagogue in a suburban neighbourhood of Manchester on Yom Kippur, the day of atonement and the most solemn day in the Jewish calendar.
Police said the two people killed were Jewish.
Antisemitic incidents in the UK have soared following Hamas' October 7, 2023, attack on Israel and Israel's ensuing military campaign in Gaza, according to Community Security Trust, an advocacy group for British Jews that works to eliminate antisemitism.
More than 1500 incidents were reported in the first half of the year, the second-highest reported since the record set a year earlier.
"This is every rabbi's or every Jewish person's worst nightmare," said Rabbi Jonathan Romain, of Maidenhead Synagogue and head of the Rabbinic Court of Great Britain.
"Not only is this a sacred day, the most sacred in the Jewish calendar, but it's also a time of mass gathering."
In a series of posts on X, Greater Manchester Police said they were called to the Heaton Park Hebrew Congregation Synagogue shortly after 9:30 am local time — shortly after services were set to begin.
A caller said he saw a car being driven toward members of the public and that one man had been stabbed.
Chava Lewin, who lives next to the synagogue, said she heard a bang and thought it might be a firework until her husband ran inside their house and said there had been a "terrorist attack".
A witness told her that she saw a car driving erratically crash into the gates of the house of worship.
"She thought maybe he had a heart attack," Lewin said.
"The second he got out of the car, he started stabbing anyone near him. He went for the security guard and tried to break into the synagogue."
Minutes later, police fired shots, saying they believed they had hit the assailant.
Immediately after the attack, police declared Plato, the national code-word used by police and emergency services when responding to a "marauding terror attack".
British Prime Minister Keir Starmer denounced the "vile" synagogue assailant who "attacked Jews because they are Jews" on the holiest day of the year at a Manchester synagogue.
He flew back to London early from a summit of European leaders in Copenhagen, Denmark, to chair a meeting of the government's emergency committee.
Starmer said the nation must defeat rising antisemitism as he promised to increase security in Jewish communities.
"I promise you that over the coming days, you will see the other Britain, the Britain of compassion, of decency, of love," Starmer said.
King Charles said he and Queen Camilla were "deeply shocked and saddened" to learn of the attack on such a significant day for the Jewish community.
Manchester was the site of Britain's deadliest attack in recent years, the 2017 suicide bombing at an Ariana Grande concert that killed 22 people.
