Russian Daniil Medvedev, who won the singles title on Saturday, is among those who have been unable to leave the city because of the attacks from Iranian missiles and drones.
"The health, safety and well-being of our players, staff and tournament personnel is our priority," the ATP said in a statement published on X, formerly Twitter.
"We can confirm that a small number of players and team members remain in Dubai... They are being accommodated in the official tournament hotels.
"We are in direct communication with those affected."
Finnish player Harri Heliovaara, who won the doubles alongside British player Henry Patten, wrote on his blog on Sunday "much of the airspace in the surrounding areas is closed" in response to the Iranian strikes.
The Finn estimated that around 30 people in total were being housed in a hotel close to the airport.
"We're just calmly waiting for things to improve," he added.
"Of course we want to leave as soon as possible, but sometimes the best thing is just to wait. Things will get better from here."
The players were offered a glimmer of hope when Dubai Airports announced "limited" flights would resume on Monday evening.
Emirates and low-cost carrier flydubai both said they would resume some flights Monday evening.
Etihad Airways, which operates flights from Abu Dhabi, said it would resume operations on Tuesday.
Targeted since Saturday by American and Israeli strikes, Iran has responded by sending drones and missiles toward several countries in the region, including the United Arab Emirates.
Despite the numerous explosions heard since the beginning of the war in Dubai, the doubles final was played on Saturday and the trophy ceremony went ahead for the singles event.
The Dubai ATP 500 was the last in a series of tournaments on the men's and women's tours before they shift to California on Wednesday for the Masters and WTA 1000 in Indian Wells.
Challenger and International Tennis Federation (ITF) tournaments, at the second and third tiers of the professional circuit, are still scheduled to be held in Fujairah, in the northeast of the Emirates, in the coming days.
AFP contacted the ATP and ITF on Monday to find out whether those tournaments would go ahead but neither responded immediately.