The Spaniard was at the Aviva Stadium in Dublin on Tuesday night as the Republic of Ireland international collapsed in a heap after making a first-half challenge in his country's 3-1 World Cup qualifier victory over Kazakhstan.
Gibson was treated on the pitch for several minutes before being carried off by medics with his right knee heavily bandaged.
Interim Ireland manager Noel King later admitted the extent of the damage was not yet clear.
King said after the game: "I'm not sure. They have to review and check everything, but it wasn't nice."
However, the Football Association of Ireland had earlier confirmed that the 25-year-old would be assessed by Everton's medical staff following his return to Merseyside.
In a statement released via its Twitter account, the FAI said: "Darron Gibson has been assessed by our team doc and will return to his club tomorrow for a scan with suspected knee ligament damage."
Gibson missed the start of the season with a knee problem and any extended absence would come as a huge blow to the Toffees after their positive start to the campaign.
Ironically, he had only just returned to international action after making himself unavailable for Ireland following former boss Giovanni Trapattoni's decision to leave him sitting on the bench for the Republic's entire Euro 2012 finals campaign.
He had indicated his intention to end his self-imposed exile in the wake of Trapattoni's departure last month and was duly called up by King for the final two qualifiers against Germany and the Kazakhs.
He played the full 90 minutes in Cologne on Friday night as Ireland went down 3-0 to the Germans, but managed only 35 minutes at the Aviva Stadium on Tuesday before disaster struck.