In a statement issued on Monday, Oxfam said the temperatures are likely to rise up to 40 degrees Celsius (104 Fahrenheit) in the coming days and "The health risks must be urgently addressed".
"Increased cases of public health-related diseases such as diarrhea and skin infections have already been recorded in host communities and temporary settlements where an increasing number of refugees now live," it added.
Oxfam said it is "crucial to ensure funds are in place to provide refugees with shelter, clean water and adequate sanitation."
The aid organization added that it is aiming to raise $53.4 million (41.6 million euros) over the next year.
"Providing safe water, appropriate sanitation facilities and access to health care is costly. It's time for the key donors to wake up and face that reality," said Rick Bauer, regional humanitarian coordinator of Oxfam.
"The sad reality is that the vast majority of Syrian refugees are not going home soon. It is also crystal clear that host communities in Lebanon and Jordan need urgent help."
Bauer said Oxfam is "starting to really worry about the health of Syrian refugees".
"The aid effort must be properly funded and focused on providing refugees with affordable and decent places to stay, where they can live with dignity. That's priority number one for refugees and host communities alike," he said.
On Friday, the United Nations refugee agency announced that the number of Syrian civilians who have fled to other countries to escape violence in their homeland has exceeded 1.5 million.