The ministry condemned what it called an act of "flagrant aggression".
However, a coalition spokesman insisted that its forces had carried out no strikes in the area near the camp.
The coalition has been targeting Islamic State (IS) militants in Syria since September 2014, and does not co-ordinate with the authorities in Damascus.
The Syrian foreign ministry said four coalition warplanes fired nine missiles at the camp in Deir al-Zour province on Sunday evening, killing three soldiers and wounding 13 others.
Three armoured vehicles, four military vehicles, heavy machine-guns and an arms and ammunition depot were destroyed, it added.
The ministry did not say which camp was hit, but the Syrian Observatory for Human Rights earlier reported that coalition jets had bombed part of the Saeqa camp, near the town of Ayyash in northern Deir al-Zour.
The UK-based monitoring group put the death toll at four.
"The Syrian Arab Republic strongly condemns this flagrant aggression by the US-led coalition forces, which blatantly violates the objectives of the UN Charter," the foreign ministry warned.
The ministry called on the UN Security Council to "take urgent measures to prevent such aggressions from occurring again".
It added that such "aggression hinders the efforts to fight terrorism, and proves that the US-led coalition lacks seriousness and credibility to effectively fight terrorism".
However, coalition spokesman Col Steve Warren denied it was responsible.
"We`ve seen those Syrian reports but we did not conduct any strikes in that part of Deir al-Zour yesterday. So we see no evidence," he told the AFP news agency.
Col Warren said the only strikes in Deir al-Zour targeted a wellhead at an oil field 55km (34 miles) away from the area where the soldiers were reportedly killed.
"There were no human beings in the area that we struck yesterday," he added.
IS controls most of Deir al-Zour province, including almost all of its capital.
The province links the group`s headquarters in Raqqa with territory controlled by the group in western Iraq, and its oilfields are also a major source of revenue for IS.
If coalition jets did hit the Syrian army camp - reported to be close to ground held by IS - it would be the first time such a thing is known to have happened since the US began air strikes in Syria, says the BBC`s Jim Muir in Beirut.
The coalition has been stepping up its attacks in recent weeks on IS positions and oil installations in northern and eastern Syria.
Broadening the scope brings with it a risk that unintended targets might be hit, our correspondent adds.
Last week, the UK decided to participate in the air strikes in Syria, extending its existing bombing campaign against IS in Iraq.
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