Galloway was forced off before the interval during Everton's clash against Manchester City on Sunday and now manager Roberto Martinez has gone on to reveal that the young left-back has suffered a knee injury, which will be assessed within the next 48 hours.
"Brendan has been terrific and we as a football club are ready to give young players an opportunity," said Martinez.
"He picked up a patella tendon problem that we'll assess in the next 24 to 48 hours. It's probably more to do with his age and the fact he's still growing rather than a structural injury.
"Bryan Oviedo is fully fit and needs a bit of match fitness now. Hopefully we'll see him on the pitch very soon."