Walters has made only two substitute appearances for Burnley in the league since signing in the close season and Dyche said he would not set a timeline for the 34-year-old's return.
"Jon won't make it for the weekend as we are still letting his knee calm down," Dyche told the club's website (www.burnleyfootballclub.com) on Friday.
"We've had a view on it and it's all common sense in terms of rehab and something we know about, but the knee has flared up and there is a settling down period for that type of injury, so we are unsure on timescales," he added.
"I think it will be a bit of a while; we're not sure yet, but it's not going to be days. It'll be longer than that."
Midfielder Dean Marney, who injured his cruciate ligament in last season's defeat at Arsenal, is back training with the first team, and he is joined by new signing Nahki Wells, who had ankle surgery before the season began.
"There is some time to go yet but it's good to see them out with the group, especially Nahki. Deano knows everyone, but for Nahki it's all new and it's good to see him out there," Dyche added.
Ninth-placed Burnley have secured five points on the road this season with a win over Chelsea and draws against Liverpool and Tottenham Hotspur.
They could surpass last season's total away tally of seven points with a win at Goodison Park, although Everton have never lost to Burnley at home in the league.
(Reporting by Shrivathsa Sridhar in Bengaluru)
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