A Study About How TAK-881 is Processed by the Body and Side Effects in People With Primary Immunodeficiency Diseases

The main aim of this study is to evaluate the PK, safety, tolerability and immunogenicity of subcutaneous (SC) administration of TAK-881 in adult and pediatric participants with PIDD and compare them to HYQVIA in participants 16 years old and older. The participants will be treated with TAK-881/HYQVIA or HYQVIA/TAK-881 with the same dose and dosing interval of immunoglobulin for up to 51 weeks (for participants greater than or equal to \[\>=\]16 years) and only with TAK-881 for up to 27 weeks (for participants aged 2 to less than \[\

Inclusion Criteria * Participant must have a documented diagnosis of a form of primary humoral immunodeficiency involving a defect in antibody formation and requiring IgG replacement, as defined according to the International Union of Immunological Societies (IUIS) Committee. * Participant is 2 years to \) 5 grams per liter (g/L) at the following time points: 1. At screening (sample taken prior to prestudy IgG infusion after signing the ICF) and 2. Within 12 weeks prior to screening. * If female of childbearing potential, participant presents with a negative pregnancy test and agrees to employ highly effective form of contraception for the duration of the study. * Participant, or in the case of minors, legally designated representative(s) is/are willing and able to comply with the requirements of the protocol, including PK blood sampling, for the duration of the study. Informed Consent * The participant or, in the case of minors, legally designated representative(s) is/are willing and able to understand and fully comply with study procedures and requirements, in the opinion of the investigator. * The participant or, in the case of minors, legally designated representative(s) has/have provided informed consent/assent, if applicable, (that is, in writing, documented via a signed and dated ICF and/or eConsent, if available), and any required privacy authorization prior to the initiation of any study procedures. Exclusion Criteria * Participant has a known history of a positive result 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. Cured participants with a history of hepatitis C infection who have a negative PCR test at screening is eligible. * Abnormal laboratory values at screening meeting any one of the following criteria (abnormal tests may be repeated once to determine if they are persistent): 1. Persistent alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \>2.5\* the upper limit of normal (ULN) for the testing laboratory. 2. Persistent severe neutropenia (defined as an absolute neutrophil count \[ANC\] less than and equal to (\