Lindelof left the field of play in the 74th minute of the 1-0 victory pointing at his chest in discomfort.
The Swede crouched whilst indicating towards his chest, with medics later helping him off the pitch.
Goalkeeper and man of the match David de Gea was one of the first to come to his teammate's side, and said it was difficult to see his defender struggling.
De Gea said: "I don't know what's going on but he was feeling a bit his breathing.
"We saw already [Christian] Eriksen, [Sergio] Aguero, it's sometimes a bit difficult to see your player acting like this so it was better to change and hopefully he's completely fine.
"As soon as it was like difficult breathing he was feeling something strange, it doesn't matter the game, it doesn't matter the football, first of all it's life, it's to be safe."
Lindelof's teammates rushed to his support, including Cristiano Ronaldo, who scored the game-winning penalty moments later.
Interim United manager Rangnick gave more detail on the situation, indicating that a coming together with another player triggered Lindelof's issue.
"Yeah he had a collision, he can't even remember what it was," Rangnick said.
"But he was struggling to breathe so he said he felt pain on his chest but right now they checked him, they did all the tests and everything seems to be OK."
Lindelof was replaced by Eric Bailly in the game who joined up at centre-back with defensive partner Harry Maguire.
Maguire was also asked about the situation, and said his teammate was feeling fine post-match.
"He's in the changing room. He felt a bit of discomfort," Maguire said.
"We don't really know too much details but he seems fine in there. He felt discomfort and we all wish him well."