There is no 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.