Joanne Mariner, senior crisis response adviser with the group, called the crisis "a Muslim exodus of historic proportions."
"The urgency of the situation demands an immediate response," she said. "It is time for the peacekeeping operation in CAR to protect the civilian population, deploy to threatened areas, and stop this forced exodus."
On Tuesday, U.N. chief Ban Ki-moon warned the country risked being divided into Christian and Muslim areas, the BBC reported.
"Both Muslims and Christians have been murdered and forced to flee their homes," he said. "The sectarian brutality is changing the country's demography. The de facto partition of the CAR is a distinct risk."
The United Nations said 90 percent of the country's population is eating just one meal a day and 1.25 million people need food aid.
The U.N. World Food Program was scheduled to start airlifting food Wednesday, the BBC said.