The forward appears set to miss his team's league opener at Bilbao, with Valverde saying it was hard to see the star returning for the clash.
"He's in the recovery process and I don't know if he will be ready for the start of LaLiga," he told a news conference after a 4-0 win over Napoli in Michigan on Saturday.
"It's looking difficult."
Despite Messi's absence, Barca produced a strong performance in their final pre-season friendly against Napoli.
Antoine Griezmann scored his first goal for the club, Luis Suarez netted a brace and Ousmane Dembele was also on the scoresheet in a comfortable win.
Valverde was pleased to see Griezmann, who arrived from Atletico Madrid for €120million in July, get off the mark for Barca.
"The scorers always feed on the opportunities, the goals. We are happy with him," he said.
"He gives us a lot for unchecking and defensively works well."