The Denmark Under-21 international was stretchered off in the recent Premier League defeat at Swansea after turning his ankle and further tests highlighted ligament damage.
“Scans have subsequently revealed that Philip will undergo surgical management of the lateral ligament complex of his right ankle,” the Terriers said on their official website.
“Following his surgery, Philip will be out for approximately 12 weeks and will work closely with the medical team and fitness department.”
Billing, who joined the club’s academy at the age of 17, has made a total of nine appearances for David Wagner’s side this season, including seven in the Premier League.
Wagner added: “Phil has had surgery on his ankle (on Wednesday) and we would all like to wish him a speedy recovery.
“The focus now is to help him return fitter and stronger than before, so he is ready to help us for the rest of the Premier League season.”