The 18-year-old suffered a torn muscle in the front of his left thigh during Germany's final training session before their pre-tournament friendly against the United States in Chicago.
"It happened while I was shooting on goal. I felt it immediately," Karl told Bild.
"That was a real shock for me, since I had set myself such high goals and was in good form. Playing at the World Cup would have been an absolute dream for me.
"Unfortunately this injury has now got in the way. I have to accept that and look forward," he added.
Karl had been in outstanding form heading into the tournament and was considered the favourite to start on the right wing for Germany. The left-footed attacker had scored five goals and provided five assists in 26 Bundesliga appearances during his breakout debut season at Bayern Munich.
He was included in head coach Julian Nagelsmann's final 26-man squad on the back of that form, having impressed in a 4-0 friendly win over Finland in late May. According to the German Football Association, Karl will be replaced in the World Cup squad by RB Leipzig midfielder Assan Ouedraogo, 20.
Karl's injury was confirmed by medical staff as a muscle bundle tear, with the diagnosis ruling him out for between six and eight weeks. Bayern Munich teammate Antonio Rudiger accompanied Karl from the training pitch after the injury occurred.
VfB Stuttgart forward Deniz Undav, who was present at the session, described the moment for reporters.
"It happened during a shot, in the very last action of the final training session. When he then touched that spot, we realised something was wrong there," Undav said.
Undav added that the squad felt for the youngster given the scale of his disappointment.
"We all feel sorry for him. He's a great kid. He's done an excellent job here. But he has a huge future ahead of him and will play in many more tournaments," he said.
Karl has now returned to Munich to begin treatment with Bayern's medical staff before starting his rehabilitation programme.
"I'm still in Munich this week for initial treatment, and after that I've been given some time off. In these first days there isn't much I can do in rehab, apart from giving the injury time to heal. After that, the build-up phase will begin at some point," Karl said.
Bayern sporting director Max Eberl said the timing of the setback had hit hard across the club. According to German outlet Kicker, Bayern's medical staff have also flagged a wider pattern of muscle injuries among players from the club's academy.
Several other young players at the club, including David Santos Daiber, Guido Della Rovere, Maycon Cardozo and Vincent Manuba, have dealt with similar thigh problems this season.
Karl's absence is a blow for Germany, with Nagelsmann having viewed the teenager as a serious contender for a starting role in attack. Leroy Sane is now expected to be the player who benefits most directly from Karl's enforced absence in Germany's opening matches.
For Karl himself, the focus now shifts entirely to recovery, with the hope of returning to full fitness in time to contribute to Bayern's pre-season preparations later in the summer.