Someone saw the vehicle, the license plate of which reportedly matched up with that of the car police were searching for, and proceeded to call the police.
The car was unlocked and didn't have any signs of damage, police said.
Investigators had been searching for the car since Saturday, when Davis was reported missing.
Her stepfather, Darion Vence, told police that he was driving the car to the airport to pick up Brittany Bowens, Davis' mother, on Friday night when he pulled over to check if it had a flat tire. Vence said men in a pickup truck pulled up, knocked him out and abducted him, Maleah and his 2-year-old son before eventually allowing him and the boy to go free, according to Houston police.
Police initially said Vence wasn't a suspect, and even released a photo of him on Twitter that showed an injury to his forehead, but later labeled him a "person of interest."
"I realize there's a lot of blanks in that story, but we're hoping the public can fill in the blanks," Sgt. Mark Holbrook told reporters on Sunday.
Davis, according to police, has undergone brain surgeries that "needed a lot of care" and was recently sick.
Officials with state Child Protective Services in Houston said Davis was removed from her home in August after she suffered a head injury and was then returned to the home in February. Her two brothers also were removed over that period. All three were placed with relatives.
Authorities are continuing to search for Davis. Anyone with information is urged to contact the Houston Police Department at 713-884-3131 or Crime Stoppers at 713-222-TIPS.
Fox News' Travis Fedschun and The Associated Press contributed to this report.