Tottenham striker Solanke to miss Everton game with ankle injury
Spurs signed the England international from Bournemouth for a reported fee of £65 million this month and he played in their Premier League season opener against promoted Leicester City on Monday.
Spurs, who finished fifth last season, drew 1-1 at Leicester.
"Dom picked up a knock in the last game," Postecoglou told reporters ahead of Saturday's match. "He got through the game, but it flared up the day after, and he'll miss the game tomorrow.
"It's an ankle injury. He copped it really early on, someone went across his ankle."
Solanke scored 19 Premier League goals last season to help Bournemouth achieve their highest points total in the top flight.
Uruguayan midfielder Rodrigo Bentancur is also unavailable for the fixture as he follows concussion protocols.
Yves Bissouma will be available, however. The 27-year-old Mali international was suspended for the Leicester game after a video showing him inhaling nitrous oxide was posted on social media.
"Biss is available but we've got some options there. The whole idea of trying to bulk up the squad is for these situations. He's available for selection. The bridge building continues," Postecoglou said.
Spurs could still change their squad.
"There's probably a couple more who will go out but we've done a fair bit of work over the past 12 months and we've brought down the demographic a fair way and brought in players in line with how we want to play but there's still a fair bit we want to do," Postecoglou said.