Police initially said there was "an attack" without providing further details before later saying all causes were being investigated.
The bus appeared to have been empty at the time, the police said, with the wounded apparently on another bus situated next to it.
"A bus travelling from southern Jerusalem reached Moshe Baram street," a police statement said.
"There was apparently an explosion and the bus started burning. Another bus nearby and a private car were also hit."
Most of the injuries were said to be burn wounds and smoke inhalation.
An AFP journalist at the scene said one bus was completely burnt out while another was partially burned, with a large contingent of firefighters battling to extinguish the blaze.
The incident comes with tensions high following a wave of violence that began in October which has killed 201 Palestinians and 28 Israelis.
Most of the Palestinians killed were carrying out knife, gun or car-ramming attacks, according to Israeli authorities.
A bus bombing would mark a significant escalation in the violence.
