The invention provides a human antibody that is specific for CD38. The antibody of the invention has the ability to bind to CD38 of minipig origin and induce, by cross-linking, specific killing of cells, in particular tumor cells, expressing CD38. The invention further provides uses of this antibody for treating various disorders and conditions associated with undesired presence of CD38+ cells, including hematological and inflammatory diseases. The invention also provides diagnostic compositions and methods based on detecting the presence of CD38 in a tissue or a cell of minipig origin contacted with the antibody of the invention.