Background: Family genetic testing of patients newly diagnosed with a rare genetic disease can improve early diagnosis of family members, allowing patients to receive disease-specific therapies when available. Fabry disease, an X-linked lysosomal storage disorder caused by pathogenic variants in GLA, can lead to end-stage renal disease, cardiac arrhythmias, and stroke. Diagnostic delays are common due to the rarity of the disease and non-specificity of early symptoms. Newborn screening and screening of at-risk populations, (e.g., patients with hypertrophic cardiomyopathy or undiagnosed nephropathies) can identify individuals with Fabry disease. Subsequent cascade genotyping of family members may disclose a greater number of affected individuals, often at younger age than they would have been diagnosed otherwise. Methods: We conducted a literature search to identify all published data on family genetic testing for Fabry disease, and discussed these data, experts’ own experiences with family genetic testing, and the barriers to this type of screening that are present in their respective countries. Results: There are potential barriers that make implementation of family genetic testing challenging in some countries. These include associated costs and low awareness of its importance, and cultural and societal issues. Regionally, there are barriers associated with population educational levels, national geography and infrastructures, and a lack of medical geneticists. Conclusion: In this review, the worldwide experience of an international group of experts of Fabry disease highlights the issues faced in the family genetic testing of patients affected with rare genetic diseases.