The airline, ABX Air, said it would seek a court order to end the strike by about 250 pilots.
The Teamsters union, which represents the pilots, said the strike had caused 75 flights to be canceled. ABX operates 35 daily flights for Amazon and 45 daily flights for DHL, according to the union.
The pilots allege that ABX is understaffed and forces them to work on days off without giving them the compensatory time off that they are owed under their contract.
The airline's president, John Starkovich, said the strike is illegal and that the dispute should be settled through arbitration.
A spokesman for ABX parent company Air Transport Services Group Inc. said the company would not comment on the impact of the strike.
Neither Amazon nor DHL responded immediately to requests for comment.
Wilmington-based Air Transport Services earned $22 million in the first nine months of this year, down from $26.5 million in the same period of 2015. The company's labor costs have increased 30 percent in that time, according to a regulatory filing.
The company's shares fell 24 cents, or 1.4 percent, to $16.44 on Tuesday. They have gained 86 percent in the past 12 months.
(Associated Press / FOX News)