Liverpool manager Jurgen Klopp said goalkeeper Alisson's calf injury "cast a shadow" over the 4-1 win against Norwich in the Premier League season opener.
The Brazilian suffered the problem as he took a goal-kick towards the end of the first half, and will now miss next week's Super Cup match against Chelsea in Istanbul.
The 26-year-old former Roma player was replaced by new signing Adrian, a free agent in the summer after he was released by West Ham.
Klopp said: "Adrian was completely relaxed and did what he had to do. He's a good keeper, calm on the ball and a good shot stopper. That's why we signed him."
Liverpool's third-choice keeper Caoimhin Kelleher is recovering from minor surgery on a broken wrist.