It was not immediately clear how many people were in the two craft, a Boeing B-17 Flying Fortress and a smaller Bell P-63 Kingcobra, the Federal Aviation Administration said.
Nor was it clear whether anyone survived the early afternoon crash, which occurred during the Wings Over Dallas Airshow at Dallas Executive Airport.
While the number of casualties was not immediately known, "no spectators or others on the ground were reported injured," Dallas Mayor Eric Johnson tweeted.
Multiple videos posted on social media showed dramatic scenes of the smaller plane descending towards the lower-flying B-17, crashing into it.
After the collision, the planes appeared to break up into several large pieces before crashing into the ground and exploding in a ball of fire, creating a huge plume of black smoke.
The crash scattered debris across the airport grounds as well as on a nearby highway and strip mall, Johnson said.
The FAA said its agents and the National Transportation Safety Board would investigate the incident.
"As many of you have now seen, we have had a terrible tragedy in our city today during an airshow. Many details remain unknown or unconfirmed at this time," Johnson said.
The B-17, a four-engined bomber, played a major role in winning the air war against Germany in World War II. With a workhorse reputation, it became one of the most produced bombers ever.
The P-63 Kingcobra was a fighter aircraft developed during the same war by Bell Aircraft but it was used in combat only by the Soviet Air Force.
One of the last major crashes of a B-17 was on October 2, 2019, when seven people died in an accident at an airport in Windsor Locks, Connecticut.
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