Two workers at the auto business that was struck were still unaccounted for as of Tuesday evening, and it is not known how many customers were on the premises when the crash happened.
In a statement, UPS said three crew members were on board, adding "we have not confirmed any injuries/casualties".
A preliminary investigation is under way but officials have said it is too early to say what caused the crash.
Officials did note, though, that the massive blaze was due to the amount of fuel onboard the aircraft, which was beginning a journey of around 4,300 miles (6,920km) to Hawaii.
The aircraft was carrying 38,000 gallons (144,000 litres) of fuel when it crashed.
It has not been confirmed what cargo was on board, though officials have said the plane was not carrying anything that would create a heightened risk of contamination.
The explosion engulfed at least two nearby businesses, including a petroleum recycling company. A shelter-in-place order was initially issued for within five miles of the airport due to concerns of further explosions and air pollution, but was later reduced to just one mile.
All departing flights for Tuesday evening were cancelled, the airport said in a statement on X.
Louisville Fire Department chief Brian O'Neal said the amount of fuel spilled at the crash site made it a "very dangerous situation".
An order warning people to shelter in place was reduced from a five-mile radius from the airport to a one-mile radius as crews worked to contain the blaze on Tuesday night.