Suliyat Adulkareem, 29, gave birth to the babies, two boys, and two girls, at the Latifa Hospital for Women and Children on July 1.
They were born prematurely at nearly 31 weeks through an emergency C-section and placed on ventilators at the neonatal intensive care unit, the hospital said in a statement.
However, the family had no medical insurance and racked up more than AED 400,000 (about $108,000) in medical expenses since the quadruplets were born, their father Tijani Abdulkareem told CNN.
The Nigerian community and other nationals in Dubai rallied around them to help raise AED 42,000 (around $11,500) to pay part of the bills.
The Crown Prince stepped in to pay the bills after he came across the initial CNN report
highlighting the family's story.
He was moved by their plight and informed his office to assist the family, the hospital said.
'A huge favor'
Abdulkareem told CNN he was shocked by the ruler's generosity, and the couple have decided to name two of their babies after him.
One of the girls will also be called Latifa after the hospital, he said.
"It's just a huge favor, and we are still in shock because we didn't even know how to get the money. I had been sleepless wondering how to pay the bill," Abdulkareem said.
Abdulkareem, a chef at a restaurant in the city, said he was distressed when he discovered his wife was going to have quadruplets.