Several people were in critical condition after the first explosion at a bus stop in West Jerusalem.
One person died in the hospital, police confirmed. Several are in critical condition.
The victim was identified as Aryeh Schupak, 15, who was heading to a Jewish seminary when the blast occurred. Aryeh was also a Canadian citizen, Canada’s ambassador to Israel, Lisa Stadelbauer, confirmed.
The blasts came hours after Israeli forces killed a 16-year-old Palestinian during a night-time raid in the occupied West Bank.
Tension has been high since a string of Palestinian attacks in Israel earlier this year, in which 19 people were killed, prompting almost daily Israeli raids in Palestinian territory. At least another 10 Israelis were killed in recent attacks.
At least 100 Palestinians have been killed in the West Bank this year, making it the worst year for violence there since 2015.
Police said Wednesday's bombs were activated remotely and could have killed many more people. Officers are searching for the perpetrators and conducting “intensive” ground and air searches.
Magen David Adom, Israel’s ambulance service, said it had treated seven patients and transferred many wounded to various Jerusalem hospitals.
At least one explosives expert was seen at the scene of the blast at the bus stop, witnesses said.
The blasts come as Israel prepares to usher in a new government, poised to be one of the most right wing in its history.
Itamar Ben-Gvir, a key member of prime minister-elect Benjamin Netanyahu's winning bloc, called for tougher action on Palestinian attackers following the bombings.
“It's time to take a hard hand against terrorists, it's time to make order,” he wrote on Twitter.
He later travelled to the site of one of the blasts, telling a crowd: “We must exact a price from terrorism. We must return to targeted killings, we must impose a curfew on the village from which the terrorists came, we must stop the camps in the security prisons.”
“It's time to establish a right-wing government as soon as possible. Terror does not wait.”
The Otzma Yehudit chief was previously banned from public office for inciting racism and has called for the death penalty for Palestinian attackers.
Despite an increase in violence in the Israeli-occupied West Bank this year, bombing attacks have become very rare since the end of the Second Intifada nearly two decades ago, a five-year period of violence that left 3,000 Palestinians and 1,000 Israelis dead.
This year is the deadliest in the West Bank since 2006, with more than 130 killed so far as Israel continues crackdowns in what it says is an attempt to root out terrorist groups responsible for attacks on soldiers and civilians.
Israel captured the West Bank in the 1967 war and has since maintained a military occupation in the territory and settled more than 500,000 people there. It is expected to legalise more Israeli outposts once the new government is confirmed.
Also on Wednesday, Defence Minister Benny Gantz announced the closure of checkpoints to the West Bank town of Jenin as the army demanded Palestinians return the body of an Israeli Druze man killed in a car crash.
The Gilboa and Salem checkpoints, used daily by thousands of Palestinians who work in Israel, were closed after the remains of a high school pupil were taken from a Jenin hospital. Other Israelis injured in the accident had been transferred to a hospital in Haifa.
“The body was taken from the hospital in Jenin and is expected to be returned to Israel shortly, as a required humanitarian act,” the military said.
Jenin has been a flashpoint for violence in recent months as Israel has taken aim at the group the Jenin Brigades, which it says is behind some of the recent attacks in Israel. It has launched similar crackdowns in Nablus, home to the Lion's Den group, which has claimed responsibility for several attacks.
Sixteen people were arrested in Israeli raids in Nablus on Wednesday morning, the army said.
Israel says its almost nightly arrest raids in the West Bank are needed to dismantle militant networks at a time when Palestinian security forces are unable or unwilling to do so.
But Palestinians say the raids undermine their security forces and are aimed at cementing Israel’s open-ended 55-year occupation of lands Palestinians want for an independent state.