It comes days after a US warplane shot down a Syrian government fighter jet in the north of the country, prompting a furious reaction from Russia.
Russia accused the US-led coalition of "complicity with terrorism".
"In Syria this type of strike is akin to complicity with terrorism," Russia's deputy foreign minister Sergei Ryabkov told the Interfax news agency.
Moscow has now suspended an incident hotline intended to prevent confrontations in Syria's crowded air space, and warned it could consider US-led coalition planes "targets".
The rising tensions prompted Australia to announce it was suspending its participation in air missions over Syria as part of the US-led coalition fighting the Islamic State group.
In Tuesday's incident, the US-led coalition said an F-15E Strike Eagle jet destroyed an armed Shahed-129 drone in the early hours of the morning as it neared the Al-Tanaf base along Syria's eastern border.
"It displayed hostile intent and advanced on Coalition forces," the statement said.
A US military official told AFP the drone was "on a run toward our folks to drop a munition on them" and was shot down in self-defence.
US presence 'illegal': Russia
Coalition forces are using the Al-Tanaf base by Syria's borders with Jordan and Iraq to train anti-jihadist Syrian fighters and stage attacks against IS.
But their presence there has led to a series of confrontations with pro-regime forces, including on June 8 when a US plane also downed a drone after it dropped munitions near Al-Tanaf.
That incident followed two others involving US fire against pro-regime forces on the ground as they came close to the garrison.
Image courtesy: Operation Inherent Resolve Source: Operation Inherent Resolve
Tensions have also flared between US forces and the Syrian regime further north, where the coalition is supporting an alliance of Kurdish and Arab fighters battling to oust IS from the city of Raqa.
On Sunday, a US fighter jet downed a Syrian government warplane for the first time in the country's conflict south of Raqa, sparking an angry reaction from regime ally Russia.
Moscow said it was suspending an incident hotline set up two years ago and warned that it would consider international aircraft operating in central Syria "aerial targets."
Washington said it would "work diplomatically and militarily... to reestablish deconfliction" but Moscow continued to take a hard line Tuesday even before the latest incident.
"It is absolutely illegal," Russia's Deputy Foreign Minister Mikhail Bogdanov said Tuesday of the presence of American forces in Syria.
"There has been neither a Security Council decision, nor a request from the official authorities of the Syrian Arab Republic as a sovereign state," Russia's Interfax news reported.
Risk of escalation
The growing tensions come as the coalition supports the Kurdish-Arab Syrian Democratic Forces (SDF) fighting to take Raqa from IS.
The SDF now control four neighbourhoods in the city, and on Tuesday also advanced along its southern outskirts, moving closer to completely encircling Raqa.
Syria's government is not involved in the operation and is instead looking further east to the largely IS-held oil-rich province of Deir Ezzor.
Its forces are moving on three fronts, south of Raqa city, through the central Badia desert region, and along the eastern border.
And it is on the Raqa and eastern border fronts where the advances have brought the regime into conflict with US-led forces.
On June 9, despite the series of engagements with US forces at Al-Tanaf, the regime skirted around the base to arrive at the Iraqi border for the first time since 2015.
The move effectively blocks international forces and their local partners in the garrison, and prevents them from themselves advancing towards Deir Ezzor.
READ THESE TOO
Russia issues warning after US shoots down Syrian jet
Despite the increasing number of incidents, analysts say neither Syria's regime nor Washington currently wants a major confrontation.
"It doesn't look like anyone currently intends to deliberately escalate further, but when you've got these little skirmishes... the risk is that you can end up in an escalation by accident," said Sam Heller, a Syria expert at The Century Foundation.
More than 320,000 people have been killed since Syria's conflict began with anti-government demonstrations in March 2011.
It has became a complex war drawing in multiple foreign players, including Russia, which launched a military campaign to support the regime in 2015 that has helped the government recapture large swathes of territory.
