The 19-year-old was carried off the pitch on a stretcher with his neck in a brace during the closing stages of the game after colliding with his own goalkeeper Ederson.
It is understood that Garcia was conscious in the City dressing room after the final whistle but medical staff transported him to hospital to undergo tests on the potential injury.
Pep Guardiola said he was “very concerned” by the injury to Garcia, whose lengthy on-pitch treatment led to 11 minutes of stoppage time being added on at the end of the second half.
“We are concerned about Eric of course,” Guardiola said. “He is conscious but I think he is going to be tested tonight because a kick in the head is always so dangerous.
“The doctor told me he was conscious and then they asked me to be with (the media). I’m pretty sure we’re going to do absolutely everything to be sure that everything is fine and well.”
The incident happened in the 81st minute when Ederson rushed off his line to clear a long, bouncing kick by his opposite number Bernd Leno.
The City goalkeeper said on Instagram: “Garcia, after a big scare, I hope to see you tomorrow to apologise. Stay well in safety!”
Garcia, a highly-rated young centre-half, was making only his third Premier League start having been preferred over Nicolas Otamendi, Fernandinho and John Stones.
Phil Foden, who scored the third goal of the evening in time added on for Garcia’s injury, said the City players did not see Garcia at full time.
“No one saw him after the game, but I asked the doctor and he said he’s doing well at the moment,” Foden said.
“Hopefully nothing serious has happened. He’s going for a scan to see if anything is broken. It looks good at the moment, fingers crossed.”