The Paris Saint-Germain forward had to have his right ankle wrapped in ice as he was carried down the tunnel after just 20 minutes of a pre-tournament friendly.
Neymar was seen crouched on his own on the pitch just moments before going off, and didn't appear to have suffered the injury through any hard contact.
The injury occurred after Everton star Richarlison scored the opener in Qatar, as he converted an open header to break the deadlock.
Straight after the ball hit the net, and while his team-mates were celebrating, Neymar walked to the tunnel and was immediately seen to by medical staff.
After hobbling over to the touchline, he walked back to the substitute's bench and was treated for the ankle problem, before being carried down the touchline.
According to Brazilian journalist Raphael Zarko, Neymar left the stadium just minutes after he was carried off.
Neymar has only recently recovered from a foot injury, having missed 13 games in Ligue 1 between January and March.
Just days ago in training, he hobbled out of training after turning his left knee.
The latest injury caps off a rough week for the Brazilian, who was also stripped of the captaincy in favour of Dani Alves.
And in the first game since, Neymar lasted just 16 minutes before being carried off.
The match was a warm-up tie ahead of the upcoming tournament, which will be held in Brazil.
The hosts get the tournament underway next Saturday against Bolivia.
In a statement, the Brazilian Confederation of Football confirmed the star would miss the Copa America.
"After suffering a sprain in his right ankle during last Wednesday's game against Qatar, Neymar was evaluated and subjected to complementary imaging tests that confirmed ligament rupture in the ankle," the statement read.
"Due to the seriousness of the injury, Neymar will not have the physical conditions and sufficient recovery time to participate in the Copa América Brasil 2019.
"As of this Thursday (06), the technical committee of the Brazilian National Team will begin the definition of a substitute."
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