Lionel Messi has been ruled out of Barcelona's game against Real Betis on Sunday after suffering a setback in his return from a calf injury.
Messi originally sustained the knock earlier this month and missed Barca's tour of the United States and their 1-0 defeat to Athletic Bilbao in the league last Friday.
He returned to full training earlier this week and was expected to be in the squad for Betis' visit this weekend, but felt some discomfort when training on Friday. Barca then took the decision for the Argentina forward to train alone on Saturday.
"We can't take a step back with his recovery," Valverde said in a news conference. "If Messi is not 100 percent, he will not play."
Messi has not played a competitive game since Argentina beat Chile in the third-place playoff at the Copa America in July.
Suarez and Dembele, meanwhile, were both injured in Barca's surprise opening day defeat at San Mames last Friday. The Uruguay striker will be out until after September's international break and Dembele is set to be sidelined for five weeks.
Dembele angered the club by not revealing the extent of his pain after last Friday's game, with the severity of his injury only being established at training on Monday.
Sporting director Eric Abidal met with the France forward's agent on Friday to translate Barca's disappointment in the player, whose professionalism away from the pitch also threw up questions last year.
Valverde refused to be drawn on events, saying that "a big deal" is made of everything Dembele does and that he would not comment on the issue.
Antoine Griezmann, therefore, is the only fit forward in the first team. B team attackers Carles Perez and Ansu Fati have been training with the squad this week and could feature against Betis after included in Valverde's 18-man squad.
Barca's shortage in attack shows why they are still attempting to bring Neymar back to the club, with a third and possibly final offer expected to be made to Paris Saint-Germain in the coming days.
"Neymar's a PSG player and we have to focus on Sunday's game, which we're obliged to win after losing our opener," Valverde said.
"It's not something which affects us. If we were affected by all the rumours out there, we wouldn't be able to play.
"We're used to it and you have to be able to deal with these things."