The retired driver's sister, Kelley, tweeted that those on board were OK.
"Everyone is safe and has been taken to the hospital for further evaluation. We have no further information at this time. Thank you for your understanding," she wrote.
Earnhardt spent a few hours at a hospital before he was released.
The Federal Aviation Administration said a Cessna Citation rolled off the end of a runway and caught fire after landing. It said it received no reports of injuries.
The FAA said two pilots and three passengers were aboard.
The plane's tail number was N8JR, the FAA said. During his career, Earnhardt drove a car with the number 8 for many years.
Chief Carrier told CNN that all five people were out of the plane when the fire department arrived.
"When our first unit arrived, there were heavy flames coming from the airplane," said Carrier. The fire burned for 20 minutes.
Carrier says they were transported to Johnson City Medical Center as a precaution.
The jet crashed through a fence, the chief said. The airplane fuselage was wrapped with a portion on the fence when it came to a stop.
"If the fence had blocked the exit that could have been really bad," Carrier said during an evening news conference. "They were very lucky."
The aircraft was on fire when the pilots and passengers escaped, Carrier said. He described the aircraft as "pretty much destroyed."
When a reporter asked about Earnhardt's condition, the fire chief noted, "He was having a little bit of trouble. They transported him non-emergency."
The National Transportation Safety Board is sending two accident investigators.
Bristol Motor Speedway is about 15 miles from the airport. Earnhardt, a team owner in the circuit's second level and an auto racing analyst, was likely headed to NASCAR events there.
The Monster Energy Series will hold one of the most popular races of the season Saturday night on the .533-mile track.
Earnhardt's teams in the XFINITY Series will race Friday night. Earnhardt was scheduled to race one of the cars in Darlington, South Carolina, on August 31.
The airport remains closed while authorities investigate the crash and attend to a fuel spill.
In 2017, Earnhardt, 44, was voted as NASCAR's most popular driver for the 15th straight year.
Earnhardt, son of the late racing legend Dale Earnhardt, is a NASCAR analyst for NBC.
A network spokesperson said: "We're incredibly grateful that Dale, his wife, Amy, daughter, Isla, and the two pilots are safe following today's accident. After being discharged from the hospital, we communicated with Dale and his team, and we're all in agreement that he should take this weekend off to be with his family. We look forward to having him back in the booth (September 1) at Darlington."
Earnhardt has survived a fiery crash in the past.
In 2004, he was driving a Corvette during a practice session at an American Le Mans Series race at the Sonoma Raceway in California. After a seemingly innocent looking one vehicle wreck, Earnhardt's car suddenly burst into flames -- engulfing his yellow Corvette in fire. In multiple interviews since that accident, Earnhardt credits a spiritual being for pulling him out of the fire to safety.
CNN's Jamiel Lynch and Phil Gast contributed to this report.