Cloning Prohibition Act of 2001 - Amends the Federal Food, Drug, and Cosmetic Act to prohibit any person (including governmental entities) from: (1) using or attempting to use human somatic cell nuclear transfer technology, or the product of such technology, to initiate a pregnancy or with the intent to initiate a pregnancy; or (2) shipping, mailing, transporting, or receiving such product knowing that it is intended for such use.

Sets forth registration requirements for individuals who intend to perform human somatic cell nuclear transfer technology, including attesting that such prohibitions will not be violated.

Directs the Secretary of Health and Human Services to request the Institute of Medicine to enter into an agreement to conduct a study to: (1) review the current state of knowledge about the biological properties of stem cells obtained from embryos and fetal and adult tissues; (2) evaluate the current state of knowledge about biological differences among stem cells obtained from embryos and fetal and adult tissues and the consequences for research and medicine; and (3) assess what is currently known about the ability of stem cells to generate neurons, heart, kidney, blood, liver, and other tissues and the potential clinical uses of these tissues.