• Body weight \>= 40 kg at screening.

• Vaccination against Neisseria meningitidis serotypes A, C, W, and Y; vaccination against serotypes B, according to national vaccination recommendations.

• Vaccination against Haemophilus influenzae type B and Streptococcus pneumoniae, according to national vaccination recommendations.

• For participants continuing to receive other therapies concomitantly with crovalimab (e.g., immunosuppressants, corticosteroids, mammalian target of rapamycin inhibitor (mTORi) , or calcineurin inhibitors): stable dose for \>=28 days prior to screening and up to the first crovalimab administration.

• For female participants of childbearing potential: an agreement to remain abstinent or use contraception.

• Female participants of childbearing potential must have a negative serum pregnancy test result within 7 days prior to initiation of crovalimab.

• Participants with a prior kidney transplant are eligible if they have a known history of complement-mediated aHUS prior to the kidney transplant.

• Onset of initial TMA presentation within 28 days prior to the first dose of crovalimab (for Naive Cohort only).

• Documented treatment with either eculizumab or ravulizumab (for Switch Cohort only).

• Clinical evidence of response to a C5 inhibitor (for Switch Cohort only).

• Known C5 polymorphism (for C5 SNP Cohort only).

• Poorly controlled TMA following treatment with another C5 inhibitor (for C5 SNP Cohort only).