The US military denied any involvement.
The Syrian Observatory for Human Rights said that the strikes took place in Deir Al-Zour province, which is largely held by the Jihadist group Islamic State.
If confirmed, it would be the first coalition strike to have killed Syrian government forces.
The UK-based Syrian observatory said 13 military personnel were also wounded.
The strike hit part of the Saeqa military camp, near the town of Ayyash.
The area is largely under the control of the Islamic State of Iraq and the Levant (ISIL), and the US-led coalition has regularly targeted the group in the eastern province.
Syria’s air force is active in the region and its ally Russia also began launching strikes in the country in late September.
Syria’s Foreign Ministry said on Monday that four fighter jets from the US-led coalition targeted a Syrian Army camp with nine missiles, killing three soldiers and wounding 13 others.
The Ministry said it sent letters to the United Nations denouncing the attack on its forces.
“The Syrian Arab Republic strongly condemns this flagrant aggression by the US-led coalition forces, which blatantly violates the objectives of the UN charter,” a Ministry statement said .