Barry was substituted at half time after picking up a groin strain in the 4-0 league defeat to Liverpool, while Stones was forced from the field minutes later through illness.
The Toffees pair are now likely to miss the trip to Wembley to face Louis Van Gaal’s men for a place in the FA Cup final next month.
And speaking after the game at Anfield, Blues boss Roberto Martinez revealed the full extent of the duo’s departures from the field.
“Gareth Barry has injured his groin,” revealed the Blues boss. “He is very doubtful for Saturday.
“He felt it very close to half-time. Maybe he came off at the right time.
“To lose Gareth Barry through injury, then have John Stones the victim of illness with stomach cramps, and already have Jagielka injured at centre-back, we ended up with two midfielders playing in those positions.
“We need to forget this showing as quickly as we can.”
Martinez now has a selection headache in the heart of the Blues’ defence ahead of the clash with the Red Devils, with fellow centre halves Phil Jagielka and Ramiro Funes Mori injured and suspended respectively.