Shares of the Atlanta company at last check were off 9.5% to $28.63.
Chief Executive Ed Bastian said in a memo to employees that this week "the window opened for the 2020 voluntary departure programs."
"The last thing we expected this year was to be encouraging people to depart – 2020 was intended to be a year of growth," Bastian said.
"But it’s clear that the impact of the pandemic will be lengthy, and that Delta will need to be a smaller airline over the next few years."
The packages include cash severance payments, continued health care benefits, enhanced travel privileges, and career-transition support.
"We hope to see enough participation in these programs to help us avoid the need for involuntary furloughs later this year," Bastian said.
The airline industry has been hit hard by the coronavirus outbreak, the steps taken to slow the spread of the disease, and the collapse of the travel industry.
On Wednesday, Delta said it expected second-quarter revenue to fall 90% from a year earlier due to the impact of the coronavirus outbreak.
Earlier this month, Delta and its pilots union said they were working to avoid furloughs of roughly 2,300 pilots as the carrier contends with a drop in demand due to the coronavirus shutdown.
Bastian said Delta would be starting the program in Minneapolis next week, and then add Atlanta, Detroit and New York, "which will evolve into a full testing program."
Bastian also addressed the issue of racial unrest, which erupted when George Floyd, an African-American man, was killed while being arrested by Minneapolis police on May 25.
Georgia, Bastian said, is one of five states that currently doesn't have a hate-crime law. Delta joined other businesses in the state asking the Georgia General Assembly to quickly pass hate-crime legislation.