Israel's president and Prime Minister called it a terrorist attack. Police were more cautious, saying that while it was a deliberate attack, they were looking at all possibilities, including that it was a criminal act.
All of those hurt were on the bus that contained the explosive device, which was on the back of the bus, Jerusalem District Police Commander Yoram HaLevi told CNN affiliate Ch.2 Israel.
At least two of the victims were seriously wounded.
"We will discover who prepared this explosive charge, we will reach those who sent them and those behind them, we will hold these terrorists accountable," Prime Minister Benjamin Netanyahu said.
There was no immediate claim of responsibility. Hamas issued a statement praising the attack but did not take credit for it.
The explosion happened in south Jerusalem just before 6 p.m., during evening rush hour. It filled the bus with orange flames and spewed thick black smoke into the air.
It took several hours for firefighters to put out the flames. Israeli police forensics teams were later seen working on board the charred frame of the bus.
"Our prayers for a speedy recovery go out to those injured in the terror attack, being treated as we speak in hospitals across Jerusalem," President Reuven Rivlin said. "It is clear to us all that the struggle against terrorism is ceaseless. We will pursue and we will reach all those who wish us harm, until quiet is assured."
U.S. Secretary of State John Kerry condemned the attack and called for an end to the Israeli-Palestinian conflict, saying Monday that it "underscores the importance of ending this conflict, so that Israelis and Palestinians can once and for all live side by side in peace and security."
The bus attack comes after more than seven months of violence between Palestinians and Israelis throughout Israel and the Occupied Palestinian Territories, though that violence has sharply declined in recent weeks.
A large number of these attacks have been stabbings, though guns and cars -- used to run over people -- also have been used. Israeli authorities have responded, at times, with crackdowns in Palestinian areas.
But it has been a decade since the last large-scale bus attack of this type in Israel. In April 2006, an Islamic Jihad suicide bomber set off a blast at the old central bus station in Tel Aviv
, killing himself and nine victims.