The suffix -ase is used in biochemistry to form names of enzymes. The most common way to name enzymes is to add this suffix onto the end of the substrate, e.g. an enzyme that breaks down peroxides may be called peroxidase. Sometimes enzymes are named for the function they perform, rather than substrate, e.g. the enzyme that joins DNA strands is called polymerase (it polymerises DNA).
This suffix was likeliest extracted from the name of diastase. It is one of a family of suffixes used to form names of particular types of chemical compounds.