The 31-year-old Manchester City loanee was left out of Thursday's 3-1 Carabao Cup victory after an unauthorised absence from training, with the club confirming that he was unavailable because of a breach of discipline.
Grealish was also missing for Monday's Premier League meeting at St James' Park, where Thierno Barry scored the only goal in a 1-0 Everton victory.
The club initially cited a lack of fitness for his latest absence, but Moyes was unwilling to provide further details when asked about the situation after the match.
"He's unavailable at the moment and we will make a decision with the club when we think that availability comes back," the Everton manager told BBC Sport.
Pressed on whether the absence was related to fitness, Moyes replied: "All I'm giving out is that he is unavailable at the moment."
The manager was equally reluctant to clarify whether the disciplinary matter had been resolved, responding: "No, I can't comment on that."
Grealish's omission from the Carabao Cup tie followed an incident understood to involve missing a training session without permission. Moyes had previously confirmed that the decision to leave him out was taken by the club and that he supported it.
The England international has been on loan at Everton from Manchester City, but his immediate return to the team remains uncertain. Moyes has not given a timetable for his availability, leaving the club to decide when the midfielder is ready to rejoin the squad.