The plane ran off the runway and crashed through a fence before coming to a halt in a field among trees and bushes.
Video footage showed firefighters spraying water onto the burning remains of the aircraft. The fuselage was reduced to ashes, with only the tail section surviving, as black smoke poured from the wreckage.
"Fortunately all 21 passengers including three crew members were reported as safely evacuated from this twin-engine jet before it was fully engulfed in flames," the Katy Fire Department said.
The McDonnell Douglas MD-87 plane was attempting take-off from Houston Executive Airport to Boston when it crashed, officials said.
Local reports said it was taking a group of fans to watch a play-off baseball game between the Houston Astros and the Boston Red Sox. Houston's KHOU news reported the plane's owner, James Alan Kent, was on board.
Tim Gibson, director of the Waller Harris county emergency services, said the passengers and crew "were stunned, they were very, very stunned, but they did all self-extricate".
He said: "We're always expecting the worst but hoping for the best. Today, we absolutely positively got the best outcome we can hope for on this incident.”
Mr Gibson said fire crews had extinguished the blaze "after substantial effort" to control burning jet fuel.
Officials said one passenger was a 10-year-old child. Two were taken for treatment for minor injuries, including back pain.
"The plane did not attain altitude at the end of the runway and went across Morton Road, coming to a rest in the field just north of the airport, where it caught on fire," Waller County judge Trey Duhon said on Facebook.