Liverpool's vice-captain was substituted during Liverpool's 3-0 win over Aston Villa.
The 24-year-old – who wore the captain's armband in Virgil van Dijk's absence – was substituted around the 70th minute of the Reds' 3-0 victory over Villa at Anfield, after receiving treatment on the field.
After leaving the pitch, Alexander-Arnold headed straight down the tunnel, while Klopp revealed the player had sustained a hamstring injury – though it appeared "not too serious".
A scan confirmed the right back had suffered a minor hamstring strain, while he also withdrew from international duty with England.
Speaking in his Friday press conference ahead of the trip to Wolves, Klopp has now confirmed that Alexander-Arnold will not be fit to take part in the game at Molineux.
He said: "He [Alexander-Arnold] is not available. We knew that before. He didn't train with the team. It's not the worst hamstring injury but it's a hamstring injury. We hope he can start, because he's running already, ball work early next week."
Speaking on how Alexander-Arnold's absence will affect Liverpool's game plan, Klopp said: "We have to be flexible. If you watch the game against Villa, Trent was not fixed in a midfield role. It must be fine, it will be fine. We must adapt to the different skillset of the player."