There is no clear timescale for Andy Murray’s return after Britain’s former world number one ruptured ankle ligaments earlier in March.
The 36-year-old sustained the injury in his Miami Open third-round defeat.
A spokesperson said Murray will miss April’s clay-court Monte Carlo Masters and BMW Open in Munich following a consultation with medical experts.
The three-time Grand Slam champion has previously said he does not plan to “play much past this summer”.
Murray played on to complete the match against Machac, losing 5-7 7-5 7-6 (7-5), before revealing the extent of the injury on Monday.
The Scot said he had suffered a full rupture of his anterior talofibular ligament and near full-thickness rupture of his calcaneofibular ligament.
He will continue to review his options with his medical team.
Murray, who turns 37 in May, said earlier this year that he wants compete at another Olympic Games before he retires.
The two-time Olympic champion has also indicated he wants to make one final appearance at the French Open, which starts on 26 May.
Murray has only played once at Roland Garros since undergoing career-saving hip resurfacing surgery in 2019, losing to Stan Warwinka in the first round in 2020.
Wimbledon, where he is a two-time champion, begins on 1 July, while the Olympics take place in Paris from 26 July.
Direct entry into the Olympic men’s singles will be given to the top 56 players in the ATP rankings on 10 June.
However, Murray could be placed outside and still qualify because of withdrawals, he could also be given a spot as a former Olympic and Grand Slam champion.
His run to the last 32 in Miami took him to 59th in the rankings before this injury setback.