The 25-year-old fell awkwardly in the first half of the Republic of Ireland's 3-1 World Cup qualifying win over Kazakhstan in Dublin, immediately clutched at his right knee and was stretchered off.
"Darron Gibson has been assessed by our team doc and will return to his club tomorrow for a scan with suspected knee ligament damage," the FAI wrote on its Twitter account.
"I saw him and he was in a lot of pain," Toffees team-mate James McCarthy told Sky Sports. "Hopefully he is okay.
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Robbie Keane scored a penalty and John O'Shea also netted in the first half for Ireland, before a late Dmitriy Shomko own goal sealed their win on Tuesday.
They were forced to come from behind after Shomko's stunning 25-yard strike in the early stages and interim manager Noel King was delighted with the reaction shown by his players, enthusing to the press: "It was a wonder goal but I thought the reaction immediately after the goal was positive.
"We got two [quick] goals to put us in a very strong position. [We] were very good, very compact when we needed to be.
"They tried to play and full marks to the team for having the courage [to do so]. The players gave everything they had."