No. Cigar boxes have traditionally been made of wood, cardboard, or paper, and while Spanish cedar is often called one of the best woods for them—praised for grain, texture, aroma, and insect resistance—it is not universal. Wikipedia notes that eucalyptus and yellow poplar have been popular substitutes (sometimes stained and scented to resemble cedar), and that other typical woods include mahogany, elm, and white oak.
In practice, many modern boxes use cedar plywood or only a thin Spanish-cedar veneer rather than solid Spanish cedar, and some premium boxes are mahogany or other woods. “Spanish cedar” itself is usually Cedrela (in the mahogany family), not a true cedar from Spain.
Source: Cigar box — Wikipedia