Drafted by Indonesia -- a non-permanent member of the Security Council -- the text drew support from 14 members, with the United States the only one to vote against.
The text stopped short of calling for fighters to be repatriated to their countries of origin -- as sought by the United States but opposed by European nations.
Instead, it encouraged UN member states to work to reinsert ex-fighters -- thousands of whom are detained in Syria and Iraq -- into society, once they have served any possible jail time, and to provide support for their families.
Washington, whose insistence on including the word "repatriation" in the text was backed by Moscow, has long defended the idea of repatriating foreign fighters detained in Syria and Iraq to their home countries.
European nations and Arab states are against the policy, preferring that they face trial and serve their sentences in the countries where their crimes were committed.
Several European countries, including France and Belgium, have adopted a case-by-case approach to repatriating the children or even wives of jihadist fighters held in the Middle East.
The decision by the US to use its veto power was striking and seemed to show Washington's growing irritation with its European partners, with whom it had until now worked to reach consensus on international affairs.
Earlier this month, the Europeans rejected a US draft resolution that aimed to extend an arms embargo on Iran as part of a US effort to re-establish international sanctions on Tehran.
"It's a real shame" that Washington opted for the veto, said one European diplomat who asked not to be named.
Last week, during a debate on counter-terrorism, the US ambassador to the UN, Kelly Craft, slammed the Europeans for "putting their head in the sand" when facing the "serious threat" posed by foreign fighters, just as she said they were doing with Iran.
The US veto was a blow to Indonesia which had made the text one of the priorities of its presidency of the Security Council this month. It called the deployment of the veto "illogical."
Some diplomats who spoke on condition of anonymity called the US move "childish."