1. Participant must have a documented diagnosis of a form of primary humoral immunodeficiency involving a defect in antibody formation and requiring immunoglobulin (IgG) replacement, as defined according to the International Union of Immunological Societies (IUIS) Committee.
2. Participant is 2 years to <16 years at the time of signing the informed consent form (ICF) for the single arm treatment part of the study OR 16 years or older at the time of signing the ICF for the crossover part of the study.
3. Participant has received regular intravenous immune globulin (IVIG) or HYQVIA with a treatment interval of every 21 or 28 days over a period of at least 12 weeks prior to screening at a minimum dose of 0.3 grams per kilograms per body weight per 4 weeks (g/kg BW/4 weeks). Variations in the treatment interval of up to ±5 days are acceptable.
4. Participant has a serum trough level of IgG greater than (>) 5 grams per liter (g/L) at screening (sample taken prior to last prestudy IgG infusion and after signing the ICF).
5. If female of childbearing potential, participant presents with a negative pregnancy test and agrees to employ an acceptable form of contraception for the duration of the study.
6. Participant/Parent/Legal Guardian is willing and able to comply with the requirements of the protocol.

1. Participant has a known history of or is positive at screening for one or more of the following: hepatitis B surface antigen (HBsAg), polymerase chain reaction (PCR) for hepatitis C virus (HCV), PCR for human immunodeficiency virus (HIV) Type 1/2.
2. Abnormal laboratory values at screening meeting any one of the following criteria (abnormal tests may be repeated once to determine if they are persistent).
3. Known history of chronic kidney disease, or glomerular filtration rate (GFR) of <60 milliliter per minute per 1.73 square meter (mL/min/1.73m^2).
4. Participant has anemia that would preclude phlebotomy for laboratory studies, according to standard practice at the site, at the discretion of the investigator.
5. Participant has an ongoing history of hypersensitivity or persistent reactions (urticaria, breathing difficulty, severe hypotension, or anaphylaxis) following IV immunoglobulin, SC immunoglobulin, and/or immune serum globulin infusions.
6. Known substance or prescription drug abuse within 12 months of screening.
7. Participant has immunoglobulin A (IgA) deficiency (IgA less than 0.07 g/L) with known anti-IgA antibodies and a history of hypersensitivity.
8. Participant has a known allergy to hyaluronidase.
9. Participant has active infection and is receiving antibiotic therapy for the treatment of infection at the time of screening.
10. Participant has a bleeding disorder, or a platelet count less than 20,000 per microliter (mcL), or in the opinion of the investigator, would be at significant risk of increased bleeding or bruising as a result of immune globulin subcutaneous (IGSC) therapy.
11. History or current diagnosis of thrombotic episodes; venous thrombus that occurred in association with a medical device >2 years prior to screening are allowed.
12. Participant has severe dermatitis that would preclude adequate sites for safe product administration in the opinion of the investigator.
13. Participant has participated in another clinical study involving an investigational product (IP) or investigational device within 30 days prior to screening.
14. Participant is scheduled to participate in another clinical study involving an IP (except for participants scheduled to enroll in a long-term follow-up study with TAK-881) or investigational device during the course of this study.
15. Participant is a family member or employee of the investigator or the investigator's site staff.
16. If female, participant is pregnant or lactating at the time of screening.

Other Protocol defined inclusion/ exclusion criteria may apply.