The blast occurred late on Tuesday in the mainly Jewish west of the city near the Hillal cafe, said eyewitnesses.
Rescue workers and police said some 40 people were injured.
The Izz al-Din al-Qassam Brigades, the armed wing of the Hamas resistance group, hailed the blast in Jerusalem and an earlier explosion near Tel Aviv, in a statement read on Aljazeera television.
“After the two attacks in Tel Arabiya (Tel Aviv) and Jerusalem, despite all the Israeli security precautions, we told the Zionists it was payback time,” read the statement.
But Hamas stopped short of claiming responsibility for the explosions.
Hours earlier, a suspected bomber detonated an explosive device outside a bus stop in Tel Aviv, leaving about eight people dead and dozens injured.
The two blasts come three days after a failed Israeli assassination attempt against the spiritual leader of the Palestinian resistance group Hamas.
That missile attack left the leader, Shaikh Ahmad Yasin, as well as about 15 Palestinians wounded and prompted calls for retaliation.
The deadly bomb blasts in Tel Aviv and Jerusalem worsened a day of bloodshed on both sides of the Israeli-Palestinian conflict.
Four Palestinians, including a 13-year-old boy, were killed in an Israeli raid in the West Bank town of Hebron earlier on Tuesday.
Meanwhile, Washington condemned the Tel Aviv and Jerusalem blasts, describing them as “vicious bombings”.
A White House statement also reiterated demands for resistance groups to be dismantled, a call rejected by the Palestinian Authority.