Previously, enzymes were thought to all be made of proteins, or proteinous in nature, however, it has been shown that not all enzymes are actually proteinous in nature.
Enzymes are more accurately defined as biological catalysts that act on chemical reactions within a cell either to influence or inhibit them.
Similar to the action of proteinous enzymes is the action of the ribozyme, which are RNA molecules that catalyze some biochemical reactions. Judging from that, not all enzymes are proteins.