CAIRO—Egypt's year of political upheaval has left a shortfall in some law enforcement, and that has been a boon for criminal organizations that traffic in human organs, a human-rights group says.

On Monday, the Coalition for Organ-Failure Solutions, a nonprofit international health and human-rights organization, is to release a new study that shines a spotlight an underground trade that world health experts say thrives here and affects thousands of African refugees in the country.

The...