Suffragettes fought to get women the vote but these rights are being eroded because of the UK's EU membership, minister Priti Patel has said.
At the launch of pro-EU exit group Women for Britain, she likened the Leave campaign to that of suffragettes.
She said those campaigning to quit the EU were fighting the "same cause" to protect "our democratic freedom".
Helen Pankhurst, great-granddaughter of suffragette leader Emmeline Pankhurst, said the comparison was "unacceptable".
"I believe that my great grandmother would have been the first to champion what the EU has meant for women - including equal pay and anti discrimination laws," she said.
The cross-party Women for Britain campaign - launched on Tuesday, International Women's Day - aims to encourage women to vote to leave the EU in the referendum on 23 June.
The group, which includes female political figures and women from the world of business, says the power of women's votes is undermined by being in the EU.
But the equivalent group trying to target women voters on the Remain side, Women In, says the benefits of being in the EU "clearly outweigh the costs".
In a video from the Britain Stronger in Europe campaign group, Education Secretary Nicky Morgan said: "From safeguarding parental leave to tackling discrimination in the workplace and bringing an end to violence against women and girls, our EU membership is critical in helping protect and further the rights of women around Britain. A vote to leave would put all of this at risk."
What is International Women's Day?
International Women's Day has been held on 8 March every year since 1913, and has been recognised by the United Nations since 1975.
The UN says it's a time to reflect on progress made, to call for change and to celebrate acts of courage and determination by ordinary women who have played an extraordinary role in the history of their countries and communities.
The theme of this year's day is "Planet 50-50 by 2030" - aiming to achieve global equality in areas such as education and end all forms of discrimination.
Read more on International Women's Day
At Tuesday's launch, employment minister Ms Patel said: "In many ways, Women for Britain are fighting for exactly the same cause. The suffragettes fought for our democratic freedom. Now we are the ones who must fight to protect it.
"Pankhurst and the suffragettes did not fight to have the right to vote on who governs them only to then see those decisions squandered to the EU's undemocratic institutions and political elite."
And UKIP's Suzanne Evans, also on the campaign's board, said EU law "takes precedence" over UK law so the institution was undermining the suffragettes' sacrifices by "taking our vote away by stealth".
Ms Patel argued that leaving the EU would "enhance our democracy and empower women" - and attacked the Remain campaign's claims that women's rights would be at risk if the UK left the EU.
She said the UK had been a world leader in promoting women's rights and opportunities, noting that it outlawed female genital mutilation in 1985 compared with 2012 in the EU.
She also said that quitting the EU would allow the UK to scrap the EU-imposed VAT on sanitary products and pave the way for cheaper car insurance, saying EU equality laws meant women could not be charged lower premiums. The UK's financial contributions to the EU could be spent on health and education, she added.
'Out of line'
Ms Patel said polls suggested 25% of women were undecided about which way to vote - more than double the number of men, and that females were regarded as more "risk averse". But she argued that the riskier option was for the UK to remain in the EU, as its destiny would be left in the hands of "faceless, unelected bureaucrats".
But Helen Pankhurst, the great granddaughter of Emmeline Pankhurst took issue with Ms Patel's comments about the suffragettes.
She said: "My great-grandmother fought tirelessly for womens' rights and dedicated her life to making sure women could live their lives free from discrimination.
"It is unacceptable to use her achievements to argue for something that is so out of line with the spirit of international solidarity that defined the suffragette movement."
Earlier, energy minister Andrea Leadsom told BBC Radio 4's Today programme it was important for women's voices to be heard in the EU referendum campaign saying the debate so far had been "quite male dominated".
The energy minister said the UK had "surrendered its sovereignty" to the EU, saying 60% of UK laws and regulations were made in Brussels.
She said women cared about issues such as the cost of living, the cost of the UK's EU membership and future prospects for themselves and their children - and argued that life outside the EU for "many people", including women, would be "much better".
"So it's absolutely not the case that the rights of women or equal opportunities would diminish in the UK if it left the EU," told Today.