The charity says a growing number of families are in desperate need of assistance this winter. It is hoped the appeal could help up to 120,000 people who have fled violence in Syria and crossed the borders into neighbouring countries.
Oxfam's Syria crisis response manager Francis Lacasse said: "Families have arrived exhausted and traumatised. Some have faced bombs and bullets to get here.
"Now they are trying to get through one of the most brutal winters in the past two decades with almost nothing. Most families have to rely on the generosity of relatives and neighbours.
"Along with local organisations, Oxfam is trying to help thousands of families through this winter, but we could do so much more if we had more funds."
It is thought 670,000 people have left Syria since the crisis began in March 2011 but numbers have risen recently, Oxfam said. In Jordan alone the number of people crossing daily trebled in the past week.
The cold weather has resulted in an increase in the number of those suffering respiratory infections and pneumonia, according to the aid agency, which is distributing mattresses, blankets, heaters and gas oil to help new arrivals.
Children, in particular, have been experiencing ill health because of the cold conditions.