Katri Kulmuni, who became the country’s finance minister this week, was criticised by a human rights group for her poll.
Her Centre Party opposes letting mothers linked to Isis return from Syria.
“Seriously, Finland? This is awful, if true,” Andrew Stroehlein, European media director at Human Rights Watch, tweeted on Thursday.
“A state should respect the rights of its citizens in all cases, not put life-and-death decisions about those citizens to a public referendum on social media. What’s next, public hangings based on the volume of stadium cheers?”
Ms Kalmuni, 32, said she had been expressing the views of the party she leads and highlighting divisions on the issue with other parties in the five-party governing coalition.
“My aim to have a discussion on social media about a complicated topic failed. I apologise for the poll,” Ms Kulmuni tweeted on Friday.
“My IG [Instagram] poll aroused condemnation, it has been removed. The style was unsuccessful.”
It came after Sanna Marin, the country’s new prime minister, said the government had given its “silent blessing” for the foreign ministry to go ahead with a plan to repatriate the children.
However, the children cannot be repatriated without their mothers because the Syrian Kurdish forces holding them oppose separating children from their mothers, Pekka Haavisto, the foreign office minister, said.
Many European countries are contemplating how to deal with citizens who travelled to Syria to marry Isis fighters.
At least 11 Finnish women and more than 30 children are being held at al-Hol camp.