The bus was attacked by armed men when it neared a checkpoint in al-Dura neighbourhood, police Captain Talib Thamir said.
The bus was carrying Shia Muslim pilgrims to religious sites
south of the capital, he said.
Four men and one woman, apparently of South Asian heritage and carrying United Kingdom passports, were taken to Yarmuk hospital in Baghdad, an official there said.
British consular officials in the capital said they were investigating the reported killings of its nationals.
"Our consular and security staff are investigating the reports," said Lisa Glover, a spokeswoman for the British embassy in Baghdad. "We've heard that it could be two British nationals, but we know no more than that."
Green Zone blast
Also on Monday morning, a mortar shell fell in the Green Zone in central Baghdad, hours before the resumption of the trial of Saddam Hussein.
There were no reports of injuries from the shell, which was fired from al-Dura, police Lieutenant Bilal Ali Majeed said.
"Our consular and security staff are investigating the reports. We've heard that it could be two British nationals, but we know no more than that"
Lisa Glover, spokeswoman,
British embassy in Baghdad
A roadside bomb also detonated next to a passing US Army
convoy in northeastern Baghdad on Monday, setting fire to a
Bradley fighting vehicle.
Police Captain Muhammad Abd al-Ghani said three soldiers were injured, but no other information was immediately available.
Aid workers kidnapped
In Canada, a parliament official said on Sunday that four humanitarian workers, including two Canadians, had been
kidnapped in Iraq but refused to name the aid organisation or say where they were seized.
Dan McTeague, parliamentary secretary for Canadians abroad, said the incident happened on Saturday.
He said he would not release those details to protect the safety of the individuals involved.
Norman Kember, a Briton, was among the four, the British
government said on Sunday. His wife said he was representing a number of groups in the country and had been a peace
activist for a long time.
Elizabeth Colton, a US embassy spokeswoman, said the
United States was investigating whether an American was among the missing four.
Rebecca Johnson, of an organisation called Christian
Peacemakers, could not confirm whether its workers were the ones kidnapped. She said they have a team of four to six people in Baghdad.
Most international organisations fled Iraq last year after a wave of kidnappings and beheadings of foreign and Iraqi hostages. Many of them were claimed by al-Qaida in Iraq, led by Abu Musab al-Zarqawi, a Jordanian.