This news is certainly not welcome and leaves Everton without another experienced central midfielder as Abdoulaye Doucoure is also out again with another hamstring problem.
Since returning to the side after over a year away on loan in France, Gomes has been filling in to some extent for the absent Mali international and has chipped in with a couple of goals from the middle of the park as well.
This is of course something Doucoure has become a real specialist in since Dyche replaced Frank Lampard last January.
Gomes' last strike was the fine free-kick that in the end saw off Crystal Palace in the FA Cup third round replay at Goodison Park which was the Blues last game.
So, losing Gomes is particularly irritating for the Toffees boss as he continues to prepare for Saturday's fourth round tie against Luton.
Scoring goals has once more become a real issue for Everton and without two players who between them have netted eight times so far this season is a considerable blow.
First-choice centre-forward Dominic Calvert-Lewin hasn't scored since the win at West Ham in October and summer signing Beto only has two goals to his name all season long.
In addition, players like Dwight McNeil (who was top scorer in the previous campaign) haven't been as prolific this term either.
It all means that the Blues have to conjure goals from somewhere else and that has also proved difficult with no other players managing more than the odd one or two.
Dyche's selection problems in midfield are further compounded by the absence of Idrissa Gueye who is on international duty with Senegal in the Africa Cup of Nations.
This situation is almost inevitable for clubs at this time of year and underlines yet again the paper-thin nature of the Toffees first-team squad.
Everton have one of the smallest squads in the Premier League and it is hitting home now on the back of a congested Christmas and New Year fixture list.
Having so many absentees (Seamus Coleman, Ashley Young and Dele are also unavailable) surely means that the Blues must think very hard before allowing any of the team to leave this month.
Several of their players are the subject of constant transfer speculation, most of all another midfielder Amadou Onana.
Rumours are rife that both Newcastle United and Arsenal are considering bids for the Belgian international this month. With all these midfield absences that now can't happen.
For a certain vintage of Evertonian, including myself, an FA Cup tie against Luton Town has very fond memories of the 1985 semi-final when the Toffees came from a goal behind to win 2-1 in extra-time.
That was the season when Everton swept all before them. Well almost all, as the final itself was frustratingly lost 1-0 to Manchester United denying the Blues an historic treble. Things are not nearly so rosy now of course.
Dyche has to weigh up the potential value of a Cup run against the possibility of more injuries to players, something he can't afford.