Opposition parties have held a series of strikes over the past month calling for Prime Minister Sheikh Hasina to hand over the control of the elections to a neutral administration.
The government has said it will move ahead with the parliamentary elections despite widespread boycotts.
Security forces blocked the front gate of Zia's house and prevented her from leaving the compound for the "March for Democracy" protest, the Wall Street Journal said.
The opposition was denied permission to march due to law and order safety concerns, police said.
Zia was seen arguing with the police officers.
"This is an illegitimate government that operates in autocratic ways," Zia said outside her house. "They have taken away people's right to vote and I call on Bangladeshis to rise up to save our democracy."
One opposition activist was shot and killed Sunday, and dozens more were injured ahead of the planned protest in Dhaka, the Journal reported.
On Saturday, government officials said they would crackdown on Sunday's protest, and police prevented many activists from reaching Dhaka.