The organization's founder is Turkish and was born in the region affected by the quake. He was also there a few days after the earthquake.
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"That 45 seconds has shaken the life of millions of people," Halil Demir said. "We have to stand with these people however we can."
The World Bank said Friday that Syria sustained an estimated $5.1 billion in damages in last month's massive earthquake that struck southeast Turkey and northern parts of the war-torn country.
The quake killed at least 50,000 people, including about 6,000 in Syria, according to the United Nations. Tens of thousands are still missing and hundreds of thousands were left homeless.
In a report released Friday, the World Bank says the level of the damage in Syria is about 10% of the country's gross domestic product.
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A Zakat worker in Turkey shared video of families moving into tents that were donated by the organization, who helped create a tent city with a long list of those waiting to get shelter. Some people have refused to leave their neighborhoods, waiting for their loved ones' remains.
"People are sleeping outside even if we have a tent village. They are waiting outside their homes," Demir sad.
Volunteers and staff packed more tents to ship Friday; the organization's shipments to the region are usually on the ground in 24 hours.
The Associated Press contributed to this report.