The Dhaka Club Cricket Organisers Association also said the election of new BCB president Aminul Islam during Monday's vote was "illegal, flawed and manipulated".
The 57-year-old, better known as "Bulbul", captained Bangladesh in their first World Cup appearance in 1999.
"We do not recognise this election," said Masuduzzaman, councillor of Mohammedan Sporting Club, at a press briefing in Dhaka.
Former Bangladesh captain Tamim Iqbal, who also attended the briefing, said the election lacked credibility.
"I found it laughable that 34 out of 42 club votes were cast through e-voting even though those voters were physically present at the polling centre," he said.
"If I had contested, I would have won easily. But (I) withdrew for the greater good of cricket."
Other councillors, including Rafiqul Islam Babu and SM Abdullah Al Fuad Redwan, joined the boycott, which they said would extend beyond Dhaka's leagues to district-level tournaments.
"We will not participate in any kind of league or district cricket from now on," Masuduzzaman said, claiming support from 38 clubs, with more expected to join.
Aminul, who secured a second term as BCB president, said his "doors were open for dialogue" with dissenting clubs.
Cricket and politics go hand-in-hand in Bangladesh and the sport has been hit by the turmoil that has wracked the country.
Former prime minister Sheikh Hasina was ousted in August 2024, fleeing by helicopter as crowds stormed her palace.
Faruque Ahmed initially took up the post as BCB president after the resignation of Nazmul Hassan, a close ally of Hasina, but it was later handed to Aminul.