Three women and one man, all in their twenties, were killed and at least 13 more were wounded, medics say.
Police said the driver had been shot dead by soldiers from the group.
Over the past 15 months there have been many attacks on Israelis by Palestinians – using knives, guns and sometimes vehicles.
A bus driver who witnessed Sunday’s attack told Israeli radio that the lorry driver had ploughed into the group before reversing over victims.
Israel’s police chief Roni Alsheich said the attacker was from East Jerusalem and owned an Israeli driving license.
Police spokesman Micky Rosenfeld said security had been heightened throughout the city in response.
The attack took place on the popular Armon Hanatziv promenade overlooking the walled Old City of Jerusalem.
Images from the scene showed a lorry with bullet holes riddled across the windscreen.
Jerusalem Mayor Nir Barkat called on residents not to “let terror win” and said militants would “pay a heavy price”.
“There is no limit to the cruelty of the terrorists who are willing to use any means possible to murder Jews and to damage the life routine of Israel’s capital,” he said.
The Palestinian militant group Hamas praised the attacker. Spokesman Abdul-Latif Qanou called it a “heroic” act and encouraged other Palestinians to “escalate the resistance”.
Before this latest incident, 35 Israelis had been killed in a wave of knife, gun and car-ramming attacks by Palestinians or Israeli Arabs since October 2015.
More than 200 Palestinians – mostly attackers, Israel says – have also been killed in that period.
Israel says Palestinian incitement has fuelled the attacks. The Palestinian leadership has blamed frustration rooted in decades of Israeli occupation.
The BBC’s Yolande Knell in Jerusalem says the number of attacks had begun to subside in recent months, but Sunday’s incident is one of the most serious there has been.