Inclusion Criteria:  The participant must voluntarily sign an Institutional Review Board (IRB)/Independent Ethics Committee/Research Ethics Board approved informed consent form after all relevant aspects of the study have been explained and discussed with the participant.  The participant has Fabry disease as confirmed at screening by the following criteria using a dried blood spot (DBS) assay:  For male participants, Fabry disease is confirmed by a deficiency of alpha-galactosidase A (GLA) activity and a mutation in the GLA gene For female participants, Fabry disease is confirmed by a mutation in the GLA gene The participant is 18 to 65 years of age, inclusive. Female participants must have a negative pregnancy test at screening. Female participants of child-bearing potential must agree to use a medically acceptable method of contraception at all times during the study and for at least 14 days after the final study infusion; the methods of acceptable contraception are listed in the protocol. The participant is deemed, as determined by the investigator, to have adequate general health to undergo the specified protocol-related procedures and to have no safety or medical contraindications for participation. The participant has not received any treatment (approved or investigational) specific to Fabry disease, such as enzyme replacement therapy (ERT), chaperone therapy, or substrate reduction therapy. The participant must have an eGFR of 45 to 120 milliliter per minute per 1.73 square meter (mL/min/1.73 m^2); eGFR will be calculated by a Shire-designated laboratory using the CKD-EPI formula. If the eGFR measurement at screening is not within the range, a second eGFR measurement may be completed and, if in range, used as the screening value. If a second measurement is taken, a minimum of 1 week and maximum of 30 days should separate it from the first. This inclusion criterion follows the European Guidelines for Treatment of Fabry Disease and Kidney Disease Improving Global Outcomes guidelines for classification of renal disease. The participant has left ventricular hypertrophy (LVH), where LVH is defined as left ventricular mass index (LVMI) greater than (>) 50 gram per square meter (g/m^2.7) confirmed by cardiac magnetic resonance imaging (cMRI) at screening. The cMRI value at screening will serve as the baseline value.  Exclusion Criteria:  In the opinion of the investigator, the participant's life expectancy is less than or equal to (<=) 5 years. The participant has undergone or is scheduled to undergo kidney transplantation or is currently on dialysis, or has any signs or symptoms of end stage renal disease. Protein/creatinine ratio (PCR) greater than (>) 0.15 milligram per milligram (mg/mg) female and > 0.14 mg/mg male. Participants who have clinically relevant history of allergy or signs or symptoms of severe hypersensitivity, (including hypersensitivity to the REPLAGAL active substance or any of the excipients), which in the investigator's judgment, will substantially increase the participant's risk if he or she participates in the study. Cardiac fibrosis involving more than 2 segments, as determined by cMRI at screening. In the opinion of the investigator, the participant has non-Fabry disease-related cause of end-organ (renal, cardiac, central nervous system) dysfunction/failure or is receiving medications that may affect the rate of disease progression, as assessed by cardiac and/or renal measures. The participant has a positive test at screening for hepatitis B surface antigen, positive test for hepatitis B core antibody, positive test for hepatitis C (HCV) antibody with confirmation by HCV-ribonucleic acid polymerase chain reaction testing, or positive test for human immunodeficiency virus antibody. Treatment with REPLAGAL at any time prior to the study.  Prior treatment with any of the following medications:  FABRAZYME (agalsidase beta) and its biosimilars GLYSET (miglitol) ZAVESCA (miglustat) CERDELGA (eliglustat) GALAFOLD (migalastat) Any investigational product for treatment of Fabry disease  Treatment at any time during the study with the following medications:  Chloroquine Amiodarone Monobenzone Gentamicin The participant is pregnant or lactating. The participant has a body mass index > 39 kilogram per square meter (kg/ m^2). (Body mass index [BMI] = kg/ m^2). The participant is treated or has been treated with any investigational drug within 30 days of study start. The participant is unable to understand the nature, scope, and possible consequences of the study. The participant is unable to comply with the protocol, eg, uncooperative with protocol schedule, refusal to agree to all of the study procedures, inability to return for evaluations, or is otherwise unlikely to complete the study, as determined by the investigator.