The 31-year-old started alongside Pierre-Emile Hojbjerg in his side's opening Group D match against Tunisia on Tuesday but only lasted 45 minutes before having to be replaced.
Delaney underwent a scan on the issue on Wednesday, and manager Kasper Hjulmand told reporters that he was 'hopeful' that the midfielder had avoided a serious problem.
However, Denmark have now confirmed that Delaney has been forced to leave the camp due to his knee issue, which will take around four weeks to heal.
"We will miss him, both on and off the pitch. Other players are ready and we have a strong squad for the next matches," Hjulmand told Denmark's social media channels following the news.
Delaney made his 72nd appearance for Denmark in their 0-0 draw with Tunisia, but he has only started two La Liga matches for Sevilla in the 2022-23 season.
Hjulmand's side - who sit third in Group D - now prepare to meet reigning champions France on Saturday before tackling Australia on November 30.