The three-member committee's tenure was to be reviewed after the World Cup, but former Test captain Bari said they had decided to quit and shoulder some of the blame for the poor performances.
"We just thought morally we were bound to do this," he told Reuters.
Bari has served as a national selector since 1998, picking teams for three World Cups.
"Coach Bob Woolmer paid a heavy price for a failed campaign," selector Iqbal Qasim said. "This is what we should have done earlier."
Woolmer died of a suspected heart attack on Sunday a day after Pakistan lost to Ireland and crashed out of the tournament.
A Pakistan cricket official also confirmed PCB Chairman Nasim Ashraf had also submitted his resignation.