Arthur's contract expired after last month's World Cup, won by hosts England, and the South African had asked for a two-year extension.
But Pakistan Cricket Board chief Ehsan Mani said Arthur and his assistant coaches Grant Flower and Azhar Mahmood had all been shown the door.
Reports say Arthur has been shortlisted as the next England coach after Trevor Bayliss departs following the ongoing Ashes Test series.
"PCB will be immediately undertaking a robust recruitment process after it decided not to renew the contracts of head coach Arthur, bowling coach Azhar Mahmood, batting coach Grant Flower and trainer Grant Luden," the board said in a statement.
Pakistan's new coaching staff will be appointed after a four-member committee assesses the team's performance at the World Cup, it said.
Pakistan lost heavily to arch-rivals India at the World Cup but finished with a record of five wins from nine matches, including one game that was rained off.
They scored 11 points were unlucky to be pipped to the semi-finals by New Zealand -- who also had 11 points -- on net run-rate.
The PCB committee, which includes former captains Wasim Akram and Misbah-ul-Haq and which met on Friday, was unanimous in calling for new coaches.
"The committee comprised of individuals who possess tremendous acumen, experience and knowledge," Mani said.
"The unanimous recommendation of the committee was that it was time for new leadership and a fresh approach."