Turkish foreign minister Mevlut Cavusoglu said the pledge was made in a phone call between Trump and Turkish President Recep Tayyip Erdogan.
Mr Cavusoglu said: “President Trump instructed [his generals] in a very open way that the YPG will no longer be given weapons.”
Erdogan’s regime has branded the YPG militia, which has links to Kurdish rebels in Turkey, terrorists.
Turkey has long complained about the US backing of the YPG Syrian Kurdish militia.
Mr Cavusoglu said: “Our discomfort regarding the provision of weapons to the YPG was conveyed to Mr Trump once again… Trump very clearly said he had given instructions to not provide weapons to the YPG.
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“We welcome the promise of not providing weapons to the YPG, and want to see it implemented practically.”
The US has seen the YPG as a key part of its strategy to defeat ISIS in Syria.
The White House claimed that although Trump and Erdogan did not name the YPG specifically but did discuss “adjustments” to the US’ support for partners in Syria.
The YPG are seen as an extension of the Kurdish Workers Party which is outlawed and has been battling for years within its own borders.
The two leaders also discussed possible future weapons sales to Turkey from the US.
A White House statement said: “Consistent with our previous policy, President Trump also informed President Erdogan of pending adjustments to the military support provided to our partners on the ground in Syria, now that the battle of Raqqa is complete.
“We are progressing into a stabilisation phase to ensure that Isis [IS] cannot return. The leaders also discussed the purchase of military equipment from the United States.”
The news follows a warning that a new terror group could rise from the ashes of ISIS.
Islamic State 2.0 could emerge once the original terror organisation is defeated, according to experts.
Analysts have warned an “Islamic State 2” or “al-Qaeda 3.0” may be launched as the fanatical cult regroups and regenerates.
ISIS strongholds have been recaptured from the terror group in Syria and Iraq, but there are still unresolved issues in the region, such as sectarian conflict, economic hardship and religious rivalries.
Head of the Middle East and North Africa at Eurasia Group, Ayham Kamel, told CNBC: “The Islamic State is almost defeated, but a radical Islamist insurgency will remain in both Iraq and Syria as the fighters turn to traditional terrorism.”
He said: “However, losing the pillars of its state, ISIS no longer represents a strategic threat to the integrity of either Iraq or Syria. There’s even a possibility of alliances with al-Qaeda in Syria as these configurations are always fluid.”