The coalition said the Syrian Su-22 had bombed US-backed fighters battling so-called Islamic State in Raqqa province, according to the BBC.
Russia, the Syrian government’s main ally, also said it was halting communications with the US aimed at preventing such incidents.
The White House says it retains the right to self-defence in Syria.
Spokesman Sean Spicer said it was important to keep lines of communication open with Russia.
It comes at a time when the US-led coalition and the fighters it is supporting on the ground attempt to oust IS militants from the city of Raqqa, the de facto capital of the “caliphate” they proclaimed in 2014.
“Any aircraft, including planes and drones belonging to the international coalition operating west of the River Euphrates, will be tracked by Russian anti-aircraft forces in the sky and on the ground and treated as targets,” the Russian defence ministry said.
However, it stopped short of openly saying it would shoot down coalition aircraft.
Reuters news agency quoted a US military spokesman as saying it was repositioning aircraft over Syria in the wake of the incident, to ensure the safety of American crew members.
Russia also denied the US had used a communications channel before the Su-22 fighter bomber was shot down, and said it was ending a memorandum of co-operation with the coalition aimed at preventing air incidents and guaranteeing flight safety.
But the chairman of US military’s Joint Chiefs of Staff, Gen Joe Dunford, said it was seeking to re-establish the “deconfliction” communications line with Russia, adding that it had remained in use “over the last few hours”.
It is not the first time communications have been suspended between the two sides – in April, the hotline was shut down after the US launched 59 Tomahawk cruise missiles at Syria’s Shayrat airbase in response to a suspected chemical weapons attack on a rebel-held town in Idlib province.
The US and Russia had agreed to resume communications last month.
UK Prime Minister Theresa May called on Russia to continue using available measures to “reduce the chance of misunderstandings over what is a crowded airspace”, Reuters reported.