Laporte left the field on a stretcher after mistiming a challenge on Adam Webster late in the first half of the champions’ 4-0 victory at the Etihad Stadium.
Manager Pep Guardiola admitted after the game the situation “doesn’t look good” but a full prognosis was still to be delivered.
The injury took the gloss off what was otherwise a comfortable afternoon for City.
Kevin De Bruyne set the tone for a dominant display by opening the scoring after 68 seconds before the in-form Sergio Aguero struck twice and Bernardo Silva added another goal late on.
To their credit, Brighton did try to attack City but the visitors were outclassed as Guardiola’s side won without hitting top gear.
“It was a nice game from us,” said midfielder Fernandinho, who was pressed into action in defence after Laporte’s exit.
“They caused a few problems for us and that’s why the Premier League is so special – any team can cause a problem.
“The level of concentration has to be high. I’m so pleased for the way we played today and the result.”
With John Stones missing through injury, the loss of Laporte highlighted the lack of cover City have had in the centre-back positions since Vincent Kompany’s departure last season.
Guardiola, however, has said that he has faith in Brazil international Fernandinho to fill in, an option created by the summer signing of another midfielder in Rodri.
“I try just to do my job,” said Fernandinho. “I’ve been training in this position the last couple of weeks.
“We still have two centre-backs but I can play in this position. It’s not a secret for me. The key is just to understand the concept of the way we have to play.
“It was my first time and I hope I can improve and do better next time.”
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