Human Fetal Tissue Transportation Act of 1987 - Prohibits interstate importation, exportation, or transportation of human fetal tissue, except as permitted under this Act.

Requires any person who transports such tissue to notify the Secretary of Health and Human Services (Secretary) semiannually of each such transportation, with specified information.

Requires the Secretary to establish regulations restricting or prohibiting interstate importation, exportation, or transportation of human fetal tissue and the operation of human fetal tissue storage facilities as necessary to protect the public health or promote the general welfare.

Prohibits operation of a human fetal storage facility, except with a license issued under this Act. Requires the Secretary to issue or renew such license for any organization which meets the requirements of this Act. Authorizes the Secretary to limit, suspend, or revoke any license for material misrepresentations, failure to provide certain information, or failure to comply with regulations.

Authorizes the Secretary to conduct investigations or inspections necessary to carry out this Act. Requires the Secretary to furnish the Attorney General information indicating noncompliance with this Act.

Establishes penalties of fines or imprisonment for violations of this Act.

Declares that this Act shall not affect any provision of State law, except to the extent such law is inconsistent with this Act, and then only to the extent of the inconsistency.

Defines "human fetal tissue" to be matter yielded by an aborted human pregnancy and any biochemical product derived from such matter.