England are in Group D with Japan, Malaysia and Canada.
On paper, Malaysia and Japan should make it to the quarter-finals as the top two teams from the group without any problems.
Badminton England, in an announcement on Tuesday, said they had been left with no option but to pull out after three of their four singles were down with injuries.
They did not reveal who the players were but their singles shuttlers in the squad are world No. 51 Toby Penty, Johnnie Torjussen (No. 205), Harry Huang (No. 319) and Ethan Rose (No. 436).
Penty was not with the team at the Sudirman Cup in Finland last week as Torjussen had played in his absence, including in matches against Lee Zii Jia and Kento Momota in the group.
"Badminton England have today announced the withdrawal of the team which was scheduled to compete at the Thomas Cup in Denmark later this week owing to injuries to three of the four selected singles players," read the statement.
"Injuries to the top-ranked players mean that Badminton England is unable to field a competitive team and, therefore, have taken the difficult decision to withdraw from the tournament."