Public Works Minister Nisrin Barwari told journalists on Wednesday she would resign if instructed to do so by the Kurdish leadership.
"All the struggles we made last year have been lost. We've seen how democracy can be usurped," she said in reaction to the Security Council resolution, unanimously passed late on Tuesday.
The resolution endorses the transfer of power to Iraq's recently formed government by the end of June, while allowing US and other coalition forces to remain in Iraq.
But it does not endorse Iraq's interim constitution, agreed in March, which recognised special Kurdish autonomy in three northern Iraq provinces, a clause fought hard for by Iraq's two Kurdish leaders, Jalal Talabani and Masud Barzani.
Before the UN vote, Talabani and Barzani, who lead the PUK and KDP parties respectively, threatened to withdraw Kurdish officials from the interim government.
Both said Kurds would not take part in national elections next year and would "bar representatives of the central government from Kurdistan".
Barwari said she fully supported Talabani and Barzani's position and said the lack of endorsement for the interim constitution was a rejection of all minority rights.
"I'm disappointed not only as a Kurd but as a woman ... this is not what we fought for, what we committed to and what we sacrificed for - we're very disappointed in the United States"
Iraqi public works minister
"I'm disappointed not only as a Kurd but as a woman ... this is not what we fought for, what we committed to and what we sacrificed for - we're very disappointed in the United States."
She said other Kurdish ministers and senior Kurdish officials were awaiting word from the Kurdish leadership on what to do as well.
However, Iraq's most influential Shia leader Grand Ayat Allah Ali al-Sistani cautioned the UN against any reference to the charter in its resolution, threatening dire complications if they did.
Before the UN vote, al-Sistani's office said any mention of autonomy in the interim constitution "is illegal and is rejected by a majority of Iraqis".
When the interim law was adopted on 8 March, al-Sistani and Shia politicians voiced anger, allegedly over the fact Islam was not the sole basis of the charter and that Kurds were granted an implicit veto over a permanent constitution to be drafted next year.
The law gave the veto to any three Iraqi governorates which agree to object to any piece of legislation. Kurds form the majority in three governorates.