The group also called for countries to stop providing weapons to parties in Syria's conflict that are committing rights violations.
It slammed much of the international community for leaving Syria's neighbours to shoulder the burden of the massive refugee influx and said many countries were failing to donate fairly.
"The international community is falling significantly short of even the minimum required of it," the group said in a report.
"As a whole, the international community has not contributed nearly enough to the aid response, has left neighbouring countries to cope with an ever-increasing number of refugees, and has failed to unite in order to halt transfers of arms and ammunition to Syria," it added.
The group said countries like Lebanon, Turkey and Jordan -- which are sheltering millions of Syrian refugees -- were bearing a disproportionate burden.
"Oxfam is calling for a committment from rich countries in particular to offer international protection by the end of 2015 to just five percent between them of the projected total Syrian refugee population," the group said.
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That would involve the resettlement of approximately 179,500 Syrian refugees, the report added.
So far, rich countries have pledged to host just one percent of the Syrian refugee population, which climbed over three million people last month, according to UN figures.
Oxfam also urged wealthy nations to increase their aid donations for the Syria crisis, saying many rich countries were contributing far less than their "fair share" given their national income relative to other donor nations.
Russia, a staunch ally of the Syrian government, has been particularly ungenerous, according to the report, giving just one percent of what would be considered its fair share.
Countries including Britain, Denmark, Kuwait, Norway and Qatar, on the other hand, were all contributing more than 100 percent of what would be expected, Oxfam said.
The group also slammed the international community for failing to halt weapons supplies to parties committing abuses in Syria's conflict, which began in March 2011.
"The withholding of arms and ammunition from parties which are known to commit such violations is one of the clearest ways that supporters of the opposing sides can signal that egregious conduct... will not be tolerated," it said.