Palestinian militant group Hamas, which controls the Gaza Strip, praised the bombings.
“We congratulate our Palestinian people and our people in the occupied city of Jerusalem on the heroic special operation at the bus stop,” Hamas spokesman Abd al-Latif al-Qanua said.
The bombings hit amid talks on the make-up of a right-wing coalition government being formed by prime minister-designate Benjamin Netanyahu, a veteran hawk.
A key ally in the proposed alliance, far-right lawmaker Itamar Ben-Gvir, visited the scene of the blasts.
“We must form a government as soon as possible. The terror is not waiting,” he said.
The European Union’s ambassador to Israel, Dimiter Tzantchev, said he was “horrified by the terror attacks”.
The Shin Bet internal security agency told AFP the blasts were the first in Jerusalem since 2016, with 34 bombings thwarted this year.
During the second intifada, or uprising, in the early 2000s, Palestinian militants repeatedly planted bombs at urban bus stops, including in Jerusalem.
Violence has flared in recent months, particularly in the occupied West Bank, where the Israeli army has launched near-daily raids since a series of deadly attacks on Israeli targets earlier this year.
Following Wednesday’s bomb attacks, the Israeli military announced two checkpoints near the flashpoint West Bank city of Jenin had been closed.
An Israeli Druze teenager involved in a car accident in the Jenin area was abducted by Palestinian militants and died as a result, his father said on Wednesday.
“He was still alive, they took him in front of my eyes and I couldn’t do anything,” Hossam Fero told Ynet radio.
Israelis abducted dead or alive have been used in the past as bargaining chips by Palestinian militant groups to secure the release of prisoners or the return of bodies of Palestinians killed in clashes by Israel.