Two of their male colleagues from the Royal Army Medical Corps and 2nd Battalion the Duke of Lancaster's Regiment and a civilian interpreter also died in the attack.
Prime minister Tony Blair said the deaths represented the "sober and ugly reality of what is happening through terrorism in Iraq.
Eyewitnesses say the blast created a large crater in the road. At least one armoured vehicle was sighted ablaze, according to media reports.
A fifth soldier was seriously injured in the incident, an MoD spokesperson said.
Further details are not expected to emerge until the families of the four dead soldiers have been informed.
Small-arms fire claimed the lives of Kingsman Danny John Wilson, 28, on Sunday and Rifleman Aaron Lincoln, 18, on Monday. Both died in the Al-Ashara district of the city.
Today's deaths mean six British lives have now been lost in Iraq's second city during the last week. In total 140 British armed forces personnel have lost their lives serving in Iraq since the US-led invasion ousted former dictator Saddam Hussein from power in March 2003.
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