The drone, an Iranian-made Shahed 129, is the second of its type to be shot down this month.
CNN was first to report Tuesday's incident.
On June 18, a USA jet shot down a Syrian Su-22 fighter-bomber near the city of Tabqa.
Pentagon spokesman Captain Jeff Davis said it had "dirty wings", meaning it was armed.
The action was a "flagrant aggression" that confirmed the US' "real stance in support of terrorism", Syria's military said.
If Moscow is not bluffing, we could be headed for a U.S.
In backing the rebels in the early part of the Syrian Civil War, the U.S. was rather cynically engaging in a proxy war against Russian Federation, angling for regime change in Russia's main Mediterranean ally, and the host of their lone Mediterranean base.
"I'm confident that we are still communicating between our operations centre and the Russian Federation's operations centre".
The U.S. end of the line, located at the air command operations center in Qatar, remains open, Davis said, adding that the U.S. remains committed to using it.
Australian Defense Force Chief Mark Binskin said operations were halted while the Australians examined what was happening in what he had described as a "complex piece of airspace" over Syria. The Russian Defense Ministry claims that the air-safety hotline was not used and also noted that there were also Russian aircraft in the area when the plane went down.More news: Number of global displaced up to 65.6 million last year
The US-led coalition said it will defend itself against any threat.
In just over a month, USA forces have struck Iranian-backed Shiite militias in southern Syria three times, and on Sunday a U.S. F/A-18 shot down a Syrian Arab Air Force Su-22 jet.
The U.S. -led coalition said the location was close to where another "pro-regime" drone, which intelligence sources had also identified as Iranian, was shot down on June 8 after dropping bombs near coalition forces.
The US military has repeatedly warned forces fighting on Mr Assad's side to stay away from a "deconfliction zone", agreed with Russian Federation, near a garrison used by US special forces and US-backed militia around Al Tanf.
USA and Syrian forces largely had stayed out of each other's way before, because the United States operated mostly in eastern Syria and the government forces mostly in western Syria.
There are concerns that further confrontations could lead to a breakout of hostilities that would hinder the battle against the Islamic State.
Sharif said the missile launch reflected Iran's "military power", though Iran has no intention of starting another war.
Israeli security officials said Monday that they were studying the missile strike to see what they could learn about its accuracy and capabilities.
Islamic State is also facing defeat in its Iraqi stronghold of Mosul and is being forced into retreat across much of Syria, where Deir al-Zor in eastern Syria is its last major foothold.