Background: Intravenous daratumumab for treatment of patients with multiple myeloma involves a lengthy infusion that affects quality of life, and infusion-related reactions are common. Subcutaneous daratumumab is thought to be easier to administer and to cause fewer administration-related reactions. In this study (COLUMBA), we tested the non-inferiority of subcutaneous daratumumab to intravenous daratumumab. Methods: In this ongoing, multicentre (147 sites in 18 countries), open-label, non-inferiority, randomised, phase 3 trial, we recruited adult patients (age ≥18 years) if they had confirmed relapsed or refractory multiple myeloma according to International Myeloma Working Group criteria; received at least three previous lines of therapy, including a proteasome inhibitor and immunomodulatory drug, or were double refractory to both a proteasome inhibitor and immunomodulatory drug; and had an Eastern Cooperative Oncology Group performance status score of 2 or lower. Patients were randomly assigned (1:1) by a computer-generated randomisation schedule and balanced using randomly permuted blocks to receive daratumumab subcutaneously (subcutaneous group) or intravenously (intravenous group). Randomisation was stratified on the basis of baseline bodyweight (≤65 kg, 66–85 kg, >85 kg), previous therapy lines (≤four vs >four), and myeloma type (IgG vs non-IgG). Patients received 1800 mg of subcutaneous daratumumab co-formulated with 2000 U/mL recombinant human hyaluronidase PH20 or 16 mg/kg of intravenous daratumumab once weekly (cycles 1–2), every 2 weeks (cycles 3–6), and every 4 weeks thereafter (28-day cycles) until progressive disease or toxicity. The co-primary endpoints were overall response and maximum trough concentration (Ctrough; cycle 3, day 1 pre-dose). The non-inferiority margin for overall response was defined using a 60% retention of the lower bound (20·8%) of the 95% CI of the SIRIUS trial. Efficacy analyses were done by intention-to-treat population. The pharmacokinetic-evaluable population included all patients who received all eight weekly daratumumab doses in cycles 1 and 2 and provided a pre-dose pharmacokinetics blood sample on day 1 of cycle 3. The safety population included all patients who received at least one daratumumab dose. This trial is registered with ClinicalTrials.gov, NCT03277105. Findings: Between Oct 31, 2017, and Dec 27, 2018, 655 patients were screened, of whom 522 were recruited and randomly assigned (subcutaneous group n=263; intravenous group n=259). Three patients in the subcutaneous group and one in the intravenous group did not receive treatment and were not evaluable for safety. At a median follow-up of 7·5 months (IQR 6·5–9·3), overall response and Ctrough met the predefined non-inferiority criteria. An overall response was seen in 108 (41%) of 263 patients in the subcutaneous group and 96 (37%) of 259 in the intravenous group (relative risk 1·11, 95% CI 0·89–1·37). The geometric means ratio for Ctrough was 107·93% (90% CI 95·74–121·67), and the maximum Ctrough was 593 μg/mL (SD 306) in the subcutaneous group and 522 μg/mL (226) in the intravenous group. The most common grade 3 and 4 adverse events were anaemia (34 [13%] of 260 patients evaluable for safety in the subcutaneous group and 36 [14%] of 258 patients in the intravenous group), neutropenia (34 [13%] and 20 [8%]), and thrombocytopenia (36 [14%] and 35 [14%]). Pneumonia was the only serious adverse event in more than 2% of patients (seven [3%] in the subcutaneous group and 11 [4%] in the intravenous group). There was one death resulting from a treatment-related adverse event in the subcutaneous daratumumab group (febrile neutropenia) and four in the intravenous group (sepsis [n=2], hepatitis B reactivation [n=1], and Pneumocystis jirovecii pneumonia [n=1]). Interpretation: Subcutaneous daratumumab was non-inferior to intravenous daratumumab in terms of efficacy and pharmacokinetics and had an improved safety profile in patients with relapsed or refractory multiple myeloma. These data could contribute to the approval of the subcutaneous daratumumab formulation by regulatory bodies. Funding: Janssen Research & Development.