Protesters held banners reading "Let Us Live" and "Women's Strike" as they marched against the government's plans
The country's justice minister Zbigniew Ziobro said the treaty "contains elements of an ideological nature, which we consider harmful".
The right-wing cabinet says the treaty violates parents' rights by requiring schools to teach children about gender, according to reports.
Mr Ziobro said on Saturday that his ministry would ask the Ministry of Family, Labour and Social Policy to begin the withdrawal process on Monday.
The convention is formally known as the Council of Europe Convention on preventing and combating violence against women and domestic violence.
It is based on the premise that women are targets of violence simply because they are women.
It also says that men and women have equal rights and state authorities must take steps to prevent violence, protect women, and prosecute the perpetrators.
Poland's government has questioned the provision that says neither culture, custom, religion, tradition or so-called "honour" can justify violence.
Poland's right-wing ruling Law and Justice (PiS) party and its coalition partners are closely aligned with the Catholic Church.
The party has regularly criticised the treaty, ratified by a previous government in 2015, saying it contradicts Poland's constitution and Roman Catholic family traditions.
On Friday, thousands of people protested in Polish cities, carrying banners saying "Let Us Live" and "PiS is the women's hell".
Protest organiser Marta Lempart said pulling out of the treaty was a move to "legalise domestic violence".
The World Health Organisation has said domestic violence surged in Europe this year, helped by months of lockdown in many countries, aimed at limiting the spread of the coronavirus.
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