Murray hopped off court in agony late in his defeat after a third-set tie-breaker to Czech Tomas Machac.
While he continued to play and was initially optimistic about his ankle, he said on Monday that he had suffered a full rupture of his anterior talofibular ligament (ATFL) and near full-thickness rupture of his calcaneofibular ligament (CFL).
"I will see an ankle specialist when I return home to determine next steps," Murray posted on Instagram.
"Goes without saying this is a tough one to take and I'll be out for an extended period. But I’ll be back with 1 hip and no ankle ligaments when the time is right," he said.
Murray, who will be 37 in May, has already indicated he will retire later this year after battling back from hip surgery in 2019. He is likely to play at the Olympics in Paris and Wimbledon, where he has won twice, before departing from the sport.
The Scotsman is currently 62nd in the world rankings.
