"He is being interrogated to determine if he had any links with terrorists," said Inspector General of Police Tahir Alam Khan.
The suspect was arrested in Islamabad Wednesday, Dawn online reported.
At least 148 people, mostly children, were killed Tuesday when militants attacked the Army Public School in Peshawar.
"The vehicle was in the suspect's possession for the last five years," the report quoted police as saying.
However, the suspect expressed ignorance about the vehicle's use by the terrorists and said that one of his relatives had borrowed it from him.
The report also said efforts are under way to verify the suspect's claims.