The former British No 1 has not played a match since October 2020 having first experienced pain in his knee during the 2018 season.
He underwent surgery in April and was back hitting in early summer but he has not so far been able to return to competitive tennis.
He had been due to make his return in Jamie Murray’s Scotland versus England contest in Aberdeen just before Christmas but has now been forced to withdraw from that as well, with Jack Draper stepping into the England team.
A statement from organisers read: “Edmund has been forced to withdraw from the event because of a slower-than-expected recovery from the left knee injury which has kept him off the court for the last 13 months.”
It is understood the 26-year-old Yorkshireman is still hopeful of being fit for the Australian Open in January, and the same goes for Johanna Konta, who has not played since mid-August because of a groin injury having also struggled with knee problems.
Edmund reached the semi-finals of the Australian Open back in 2018, losing to Marin Cilic.
Liam Broady has been named as the fifth player for Great Britain’s Davis Cup Finals campaign later this month.
Cameron Norrie, Dan Evans, Joe Salisbury and Neal Skupski were the first four players picked by captain Leon Smith last month but the fifth slot was left open.
Andy Murray left the door slightly ajar to participating but has chosen to end his season and turn his attentions to preparing for 2022, meaning 27-year-old Broady receives his second call-up.
Britain’s group matches are being held in Innsbruck, Austria.