The former Ajax man picked up a calf problem when making his return from a long-term knee issue as a substitute in Saturday’s 1-1 draw at Brentford.
Martinez had replaced Lindelof after the Swede picked up a hamstring injury.
A difficult second season for United boss Erik ten Hag has been blighted by the consistent loss of key players to injury.
The Red Devils are sixth in the Premier League, 11 points off the top four with nine games remaining.
Martinez and Lindelof are also set to miss the FA Cup semi-final against Coventry later this month.
© Agence France-Presse
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