The international agency has urged all the armed forces to avoid use of heavy weapons in the populated areas and to provide safe exits to avoid civilian casualties.
Around 750,000 people are trapped in western Mosul with no means of safe exit ahead of Iraq's military offensive that could be launched any day, Oxfam warned in its report on Tuesday, calling on the Iraqi-led coalition to prioritise protection of civilians.
Mosul is Iraq's second-largest city which fell to Daesh in 2014. In October, the Iraqi-led coalition launched a major military offensive to drive out Daesh from the city.
The report said humanitarian conditions in western Mosul have worsened due to the supply routes being cut off following the recapture of the city's east in November.
It raised concerns for the families trapped in the city's west, particularly those living in the narrow streets of the old city which could turn into "death traps" once the military operation begins.
Despite the Iraqi prime minister's commitment to prioritise civilians safety, around 2,000 civilians were killed or injured in the first three months of the offensive to retake Mosul from Daesh, the report said.
"Over 190,000 people fled their homes, although around 30,000 have now returned," it said.
The international agency urged all the armed forces to avoid use of heavy weapons in the populated areas. It also called for provision of safe exits to avoid civilian casualties.
Citing civilian accounts, the report said, the families were not only targeted by Daesh terrorists but were caught up in air strikes during the earlier offensive to recapture eastern Mosul.