Arthur, who has been linked with a move to England, said he had done his best with Pakistan who narrowly failed to reach the World Cup semi-finals.
"I am extremely disappointed and hurt," the South African told AFP shortly after the Pakistan Cricket Board announced his departure.
"I did my wholehearted effort to lift Pakistan cricket," he added.
Arthur's contract expired after last month's World Cup, won by hosts England, and he had asked for a two-year extension.
But Pakistan Cricket Board chief Ehsan Mani said Arthur and his coaching staff, including assistants Grant Flower and Azhar Mahmood, were all out.
"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.
Reports say Arthur is on the shortlist of names for the next England coach after Trevor Bayliss departs following the ongoing Ashes Test series.
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 and 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."
The PCB said it would advertise the posts soon.
Arthur joined Pakistan in May 2016, leading them to a drawn Test series with England that lifted them to the top of the rankings.
Pakistan also won the Champions Trophy in England in June 2017, raising their stock in limited-overs cricket.
That win, Arthur said, "brought on a whole new team of young players".
"We also became world number one in Twenty20 cricket in this period, which was an achievement," he said.
However, Pakistan has wilted in Tests in the last two years, losing 2-0 to Sri Lanka in the United Arab Emirates in 2017.
In all, Pakistan won 10 out of 28 Tests under Arthur, losing 17 and drawing one.
Pakistan have also struggled in ODIs in the last two years. Under Arthur, Pakistan won 29 of 66 ODIs, losing 34 with three no-results.