The meeting comes two days after US President Donald Trump and Israel launched attacks on Iran that prompted a UN warning about child safety.
It was the first time a spouse of any serving world leader has chaired a meeting of the 15-member Security Council, the UN body charged with maintaining international peace and security.
The plan was announced last week before the launch of the US and Israeli strikes.
It comes after the US took over the monthly rotating presidency of the council, and was another sign of how Trump has personalised US foreign policy by involving friends and family in major issues.
Melania Trump's office said her aim was to emphasise education as a way to advance tolerance and world peace in the meeting, titled 'Children, Technology, and Education in Conflict'.
"The US stands with all of the children throughout the world. I hope soon peace will be yours," she said in a statement to the council on Monday.
Iran has blamed Israel and the US for a strike on a girls' primary school in the southern Iranian town of Minab on Saturday that its UN envoy Amir Saeid Iravani said had killed 165 schoolgirls. Reuters could not independently confirm the reports.
Iravani said it was "deeply shameful and hypocritical" that the US should convene a meeting on protecting children in armed conflict "while at the same time launching missile strikes against Iranian cities and bombing schools and killing children".
On Saturday, the UN children's agency, UNICEF, issued a statement noting the Iranian reports and saying the military escalation in the Middle East "marks a dangerous moment for millions of children in the region," and echoing a call by UN Secretary-General Antonio Guterres for an immediate cessation of hostilities.
Donald Trump has been a vocal critic of the United Nations since his first White House term, saying the 193-member world body was ineffective and needed reforms.
The US is billions of dollars behind in its contributions to the UN budget and the amount has grown substantially under Trump.
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