The three-time major winner, who returned from hip resurfacing surgery in 2019, said: “[It] goes without saying this is a tough one to take.”
But he added: “I’ll be back with one hip and no ankle ligaments when the time is right.”
Earlier this year, Murray, who will turn 37 in May, said he is not planning to “play much past this summer” but hopes to compete at another Olympic Games before he retires.
He indicated he wanted to make one final appearance at the French Open, which starts at Roland Garros on 26 May – nine weeks away.
Wimbledon, where he is a two-time champion, begins on 1 July, while the Olympics take place in Paris from 24 July.
Direct entry into the Olympic men’s singles will be given to the top 56 of the ATP rankings on 10 June.
However, Murray could be placed outside and still qualify because of withdrawals, and he could also be given a spot as a former Olympic champion and Grand Slam winner.
His run to the last 32 in Miami has taken him to 59th in the live rankings before this injury set-back.