Villazon was to have appeared alongside soprano Anna Netrebko and mezzo-soprano Elina Garanca in the May 3 premiere at the Vienna State Opera.
But the Mexican singer says he's being extra cautious with his schedule to ensure he makes a full recovery.
Austrian media quoted Villazon on Wednesday as saying he hopes to reschedule the Vienna performance.
Vienna State Opera director Ioan Holender said he "completely understands" Villazon's reluctance to strain his voice. Villazon announced in April that he needed surgery to remove the cyst, and cleared most of his schedule for the year.