The plane finally left for Atlanta after a short delay. It is not known if the pair were banned from the airline for refusing to wear masks.
Delta’s COVID-era policies are among the strictest among US-based airlines.
Last month, the airline announced it would require medical examinations for passengers who cannot wear face masks due to health concerns.
Delta is also insisting on pre-departure medical screenings as well as its COVID-era public health protocols.
“We encourage customers who cannot wear a mask due to a medical condition to reconsider their trip,” the airline said.
“If they decide to travel, they will be asked to fly after completing a pre-departure virtual consultation at the airport to ensure everyone’s safety, because nothing is more important.
The airline does not allow passengers to sit in the middle seats and has cut some in-flight services.