The Argentine winger has not yet fully recovered from a persistent thigh problem and will not take part in the first leg of the quarter-final tie in Cyprus
The Argentina international has been out of action for over a month with a niggling thigh injury which has seen him feature just once since the start of the calendar year.
It had been reported that Di Maria could make the squad for the continental match, but he will stay in Madrid, just like Diarra, who is suffering from a minor muscular strain.
Jose Callejon and Ricardo Carvalho have also been committed from the squad because of injury, while Xabi Alonso will have to serve a one-match ban.
On the other hand, Mesut Ozil and Pepe return to Madrid's match squad after missing the club's 5-1 thrashing of Real Sociedad on Saturday because of suspension.