Ban said he had received "troubling reports" of cluster bomb attacks on January 6 on the rebel-held capital Sanaa.
"The use of cluster munitions in populated areas may amount to a war crime due to their indiscriminate nature," the UN chief said in a statement.
Cluster bombs are banned under a 2008 international convention, although Saudi Arabia and the United States are not signatories.
The office of the UN high commissioner for human rights said Tuesday that its staff in Yemen had found remnants of 29 cluster bombs during a field visit in Haradh district in the northwest.
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It came in response to the decision by Yemen's Saudi-backed government to expel the leading UN rights official, George Abu al-Zulof.
Ban is urging the Yemeni government to reverse its decision to expel Zulof, who was declared persona non grata for an alleged lack of impartiality in his reporting.
The UN chief said he was "deeply concerned about the intensification of coalition airstrikes and ground fighting and shelling in Yemen, despite repeated calls for a renewed cessation of hostilities."
UN envoy Ismail Ould Cheikh Ahmed was in Riyadh today for talks on renewing a ceasefire in Yemen, which faces the threat of famine amid the dire humanitarian crisis.
Yemen descended into chaos when the coalition began airstrikes in March to push back Iran-backed Huthi rebels who had seized Sanaa.
More than 5,800 people have been killed and 27,000 wounded since then, according to UN figures.
The UN envoy has called for a new round of talks on January 14 but the sides have yet to confirm that they will attend.