The Brazilian forward left the field midway through the first half of Barcelona's second-leg Copa del Rey clash at Getafe after landing painfully on his right leg
Gerardo Martino allayed fears that the former Santos attacker would face an extended spell on the sidelines, with suggestions he could miss the World Cup quickly dismissed, though admitted the potentially serious injury - which is awaiting the results of scans - would rule the 21-year-old out of action for the foreseeable future.
"He won't be playing for a while, but we're relaxed about it all," said the Barca boss afterwards, dampening Neymar's hopes of playing a part in Barcelona's trip to the Etihad Stadium on February 18.
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The Blaugrana were 22 minutes into the second leg of the last-16 tie in Madrid when the forward landed painfully after crossing the ball for an attack, with replays suggesting the playmaker had suffered a really nasty injury.
Neymar had to be helped off the pitch - looking in a considerable amount of pain - at the Alfonso Perez Stadium, hobbling on his left leg with assistance from Barca medical staff.
The Brazil international was left out of the starting line-up when Martino's men faced Atletico Madrid on Saturday, though he came on as a substitute.
This was following a bout of gastroenteritis that kept him out of the first leg of the cup match with Getafe at Camp Nou, which ended 4-0 to the hosts.
Lionel Messi scored a double in that clash, which was his return to the Barca team after a lengthy spell on the sidelines, and opened the scoring on the brink of half-time in Thursday night's game following Neymar's injury.
"What happened to Neymar is a real shame," the Argentine said of his team-mate's withdrawal. "Tomorrow more tests, we hope it's nothing bad, we need him, he's important for the team."
Manchester City themselves have their own injury problems to contend with, as French playmaker Samir Nasri was ruled out for up to eight weeks - which would rule him out of the last-16 clash - though Sergio Aguero did make a goalscoring return from a calf problem on Wednesday.