The defender had to leave the 3-1 win over Reading early with a gashed foot.
Moyes told reporters at his weekly press conference: "We think it won't be too long before he is back. Hopefully we get him back quite quickly."
Jagielka has since undergone surgery to repair the wound, which was sustained during a collision with Adam Le Fondre early in the game last Saturday.
The 30-year-old will not play in Everton's home match against Wigan Athletic tomorrow lunchtime.