The Republic of Ireland international limped off 10 minutes from the end of Monday's 1-1 draw at West Brom and will be assessed at the club's Finch Farm training ground later on Tuesday.
Everton travel to League One Stevenage in the FA Cup on Saturday before heading to Anfield three days later.
"We are going to be cautious and see what the problem is, but it's not a good sign because Seamus would never want to come off the football pitch," said manager Roberto Martinez.
"He felt his hamstring, so we will have to assess it. He has been in a terrific moment of form so we will try to get him back on as quick as we can."
The 25-year-old right-back has flourished since Martinez arrived in the summer, scoring six goals, with five coming in his last 11 matches.
Everton have cover in the form of John Stones, who has also been employed at centre-back this season after injuries to Phil Jagielka and Sylvain Distin, while the out-of-favour John Heitinga is still at Goodison Park, despite being told he can find a new club in the transfer window to boost his World Cup hopes.