The stock ended the day modestly lower. During the premarket, it was down 2 percent.
The airline said that it has canceled 427 flights because of the outage. Delta also said that it has operated 1,590 of its nearly 6,000 scheduled flights so far today.
Delta CEO Ed Bastian apologized to customers in a video, saying that the airline's employees are "working around the clock" to restore normal operations.
"I apologize for the challenges this has created for you with your travel experience. The Delta team is working very, very hard to restore and get these systems back as quickly as possible," Bastian said.
Delta said in an update at 8:40 a.m. EDT that the halt on departures had been lifted and some flights were resuming. In an earlier statement, it said a power outage in Atlanta at 2:38 a.m. ET, "impacted Delta computer systems and operations worldwide, resulting in flight delays and cancellations today."
The outage affected check-in systems, airport screens and the airline website and smartphone apps.
— CNBC's Jodi Gralnick, NBC News and Reuters contributed to this report.