The two teams had been scheduled to play a Twenty20 and a one-day international on January 12 and 13 respectively, both in Lahore.
But Bangladesh Cricket Board (BCB) president Nazmul Hassan told reporters the proposed tour had been put off indefinitely amid fears over players' safety, following protests by Bangladeshis and a Facebook campaign against the visit.
Anti-Pakistan sentiment still runs strong in the country, which was part of Pakistan until 1971 when it won independence after a nine-month war.
"Bangladesh will not visit Pakistan for now. We've made the decision after considering the overall security situation in Pakistan and the concern that our people have expressed over the safety of their players," Hassan said.
"We made a commitment to visit Pakistan and it's almost mandatory for us to tour the country. But we believe safety of players and officials are of highest importance. It's a national issue."
Pakistan have had to play their "home" matches in venues ranging from Dubai to London ever since gunmen shot dead eight people and wounded seven Sri Lankan players in an audacious attack near the stadium in Lahore in March 2009.
The Bangladesh board had indicated two weeks ago that it was ready to send a team, albeit only after a final security review.
Pakistan Cricket Board chairman Zaka Ashraf had said on December 22 that Bangladesh had confirmed the tour was definitely on.
Hassan said Bangladesh had informed the Pakistan board of its change of heart and added that the team would visit Pakistan if security improves.
"We have noticed the security situation in Pakistan has not improved significantly, rather deteriorated," he said.
"We've sent a letter to Pakistan three days ago explaining our position. We've decided to wait and see."
Bangladesh had earlier agreed to tour Pakistan in April 2012 but the visit was blocked by the Dhaka high court.
Hassan said that he feared Pakistan might now bar its own cricketers from playing in the Bangladesh Premier League (BPL) in response to the decision.
The BPL is the Bangladeshi answer to the Indian Premier League -- the hugely popular Twenty20 tournament which has fused cricket with showbusiness.
In the first edition back in February, 20 Pakistani players featured in the tournament, with all-rounder Shahid Afridi fetching $700,000 in an auction of stars -- the highest amount paid.
More than 50 Pakistani players have already been bought at an auction for the second edition of the tournament, beginning on January 17.
Officials said the BPL would go ahead even if Pakistan did not allow its cricketers to play.