Paul Schwarz of the Lexington Police Department said the white Pontiac owned by 25-year-old Kelsey Peterson crossed the California border into Mexico around 11 p.m. on Tuesday.
"We know that that vehicle crossed the border and that they are probably in it or possibly in it," Schwarz said. "We've already had the FBI active on the case, so they, of course, will continue to be active on the case."
The pair disappeared after police began investigating whether they had an intimate relationship. Court documents supporting a warrant for the teacher's arrest chronicle love letters between the two.
Peterson, a sixth-grade math teacher and basketball coach at Lexington Middle School, was put on administrative leave last week, one day before the boy was last seen. A judge issued an arrest warrant Monday charging her with kidnapping, child abuse and contributing to the delinquency of a minor.
Authorities believed the two were traveling together in Peterson's car, and police nationwide and the FBI were notified about them. Court documents said the boy was last seen Oct. 26.
The boy, 13-year-old Fernando Rodriguez, was an eighth-grader at the school, but district Superintendent Todd Chessmore said he wasn't sure whether Peterson was his teacher two years ago.
The Associated Press generally does not identify people who may be victims of sex crimes, but the boy's name has been widely publicized as police search for him.
According to court documents, Fernando's aunt Laura Rodriguez told police that she talked to her nephew by phone after he disappeared, and he asked her whether a visa or passport was required to travel to Mexico.
Court documents showed authorities had recovered several e-mails and letters in which the two professed their affection for one another.
In letters, the boy called Peterson his "Baby Gurl" and said their relationship was "just not about the sex but that it was pretty good," according to court documents.
Court documents say Peterson's school-issued laptop contained letters to the student, including one from April saying she loved him, thought he loved her, was "100 percent faithful" to him and would always be faithful.
Police said the boy contacted his family over the weekend and said the two were in Grand Island, about 85 miles east of Lexington. Police have also said the pair were spotted over the weekend in Denver and Ogallala, in western Nebraska near the northeast tip of Colorado.
Peterson's MySpace Web site indicated she last logged in to the site two days before Chessmore confiscated her laptop.
"Watch your thoughts for they become words. Watch your words for they become actions. Watch your actions for they become habits," Peterson said in her profile.
Lexington, a farming and meatpacking town of about 10,000, is about 220 miles west of Omaha in central Nebraska.