Eleven shootings have taken place on or near Intestate 10 in the southwestern US state since Aug. 29, the latest of which was on Thursday when a semi-trailer was struck in the side by a bullet, police told AFP.
An investigation was also underway into another report of an attack that could be related.
The only injury has been a teenage girl who was cut by flying glass when the window of the car in which she was traveling was shattered by a bullet.
Bart Graves, a spokesman for Arizona state police, said there are fears one or more snipers may be behind the attacks.
"We think there is some copycat activity going on here, but we don't know if it's all related," he told AFP.
Colonel Frank Milstead, head of the Arizona Department of Public Safety, said the shootings amount to "domestic terrorism" and a reward of $20,000 was being offered for information leading to an arrest.
He said drivers have been lucky so far as there have been no major injuries or fatalities.
The first attacks took place on Aug. 29 when two cars and an empty tour bus were struck each by a bullet in separate incidents.
Similar attacks have since taken place.
Robert McDonald, the driver of the tour bus, said he was behind the wheel when a bullet hit the seat behind him.
"If I would have moved my head, I would have got hit," he told local media.
Arizona Governor Doug Ducey appealed to the public for information on Thursday and urged caution.
"Please be careful and stay alert," he said on his Twitter account.
Graves said that while people are scared, there has been no panic over the incidents, which recall the so-called Beltway sniper attacks of 2002 which left 10 people dead and sowed terror in Washington, DC.
"People keep driving on freeways," Graves said. "The attacks have not resulted in less traffic."