The Dhaka Metropolitan Police had issued a special notice prohibiting any form of public gathering from 4 AM tomorrow, the day of the verdict, until further orders.
The notice said inputs from intelligence agencies warned of efforts to destabilise public order, and sought cooperation from all quarters for security.
Zia, 72, and five others, including her son and Bangladesh Nationalist Party (BNP) senior vice-chairman Tarique Rahman, have been tried in the court of Dhaka's Fifth Special Judge Mohammad Aktaruzzaman on charges of embezzling 21 million takas ($252,000) in foreign donations meant for the Zia Orphanage Trust.
Zia faces up to life in prison if found guilty of the charges, which means she will be disqualified from running in parliamentary polls slated for the end of this year.
The BNP had boycotted the 2014 polls but is expected to contest the upcoming general election.
The main opposition party, which claims the charges are part of a plot to keep its leader out of the national election, has threatened to take to the streets if she is convicted.
The ruling Awami League, however, has denied it saying if Zia is not guilty, then it will be proven in court.
It has also called on its supporters to be vigilant if the BNP launches protests.
Earlier, Zia had urged her party supporters to hold "peaceful programmes".
"Please don't do something foolish that can put the party in danger. Remain united," she said last week.