The Progress party leader and finance minister, Siv Jensen, told a press conference on Monday that there had been "too many compromises" and it had become too hard to get her party's policies adopted by the four-party government.
The move means that Conservative Prime Minister Erna Solberg no longer has a parliamentary majority.
Jensen's departure was triggered by a cabinet decision, announced last week, that the woman and her two children would receive help to return to Norway so that one of the children could receive medical treatment.
The government must muster a majority in the 169-seat Storting, or Parliament. In November, Germany repatriated a woman suspected of being an IS member along with her three children.
'Over time, politics was too much based on compromises, ' said Jensen, who is Norway's outgoing finance minister.
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Most of Norway's governments since the 1970s have ruled with a minority and under its constitution the next election can not be held until September 2021.
The 29-year-old Norwegian woman, who is of Pakistani origin, was married to an Islamic State fighter.
Prime Minister Solberg said she "understood" why the Progress Party wanted to leave her coalition government, adding she would seek cooperation with the party - which is Norway's third-largest. "Our dilemma was therefore whether to bring home a child with his mother, or risk a sick five-year-old dying", she said.
Jensen said many believed that the woman, who has not been named, "used her child as a shield to come back to Norway".
Shortly after the announcement, Solberg said she intends to stay in office as the head of a minority government, although the situation is likely to make it more hard for her to govern. The parties won renewed support in 2017 elections.