Bairstow's unbeaten 108 off 48 balls, with eight fours and nine sixes, see Punjab secure the win with eight balls to spare
The Tigers were scheduled to visit Karachi at the end of the month to play one ODI and one Test.
The Bangladesh and Pakistan cricket boards have mutually agreed to postpone the tour, said in a press release issued by the PCB on Monday.
The two boards will work together to identify a future opportunity to complete the ICC World Test Championship commitment. The first Test of the series was played in Rawalpindi from Feb 7-10, which Pakistan won by an innings and 44 runs.
The PCB also indefinitely postponed the Pakistan Cup one-day tournament, which was scheduled to start from Mar 25.
Meanwhile, Bangladesh has started the Dhaka Premier Division Cricket League, the most competitive domestic cricket event of the country, from Sunday.