Background: Treatment with natalizumab once every 4 weeks is approved for patients with relapsing-remitting multiple sclerosis, but is associated with a risk of progressive multifocal leukoencephalopathy. Switching to extended-interval dosing is associated with lower progressive multifocal leukoencephalopathy risk, but the efficacy of this approach is unclear. We aimed to assess the safety and efficacy of natalizumab once every 6 weeks compared with once every 4 weeks in patients with relapsing-remitting multiple sclerosis. Methods: We did a randomised, controlled, open-label, phase 3b trial (NOVA) at 89 multiple sclerosis centres across 11 countries in the Americas, Europe, and Western Pacific. Included participants were aged 18–60 years with relapsing-remitting multiple sclerosis and had been treated with intravenous natalizumab 300 mg once every 4 weeks with no relapses for at least 12 months before randomisation, with no missed doses in the previous 3 months. Participants were randomly assigned (1:1), using a randomisation sequence generated by the study funder and contract personnel with interactive response technology, to switch to natalizumab once every 6 weeks or continue with once every 4 weeks. The centralised MRI reader, independent neurology evaluation committee, site examining neurologists, site backup examining neurologists, and site examining technicians were masked to study group assignments. The primary endpoint was the number of new or newly enlarging T2 hyperintense lesions at week 72, assessed in all participants who received at least one dose of assigned treatment and had at least one postbaseline MRI, relapse, or neurological examination or efficacy assessment. Missing primary endpoint data were handled under prespecified primary and secondary estimands: the primary estimand included all data, regardless of whether participants remained on the assigned treatment; the secondary estimand classed all data obtained after treatment discontinuation or study withdrawal as missing. Safety was assessed in all participants who received at least one dose of study treatment. Study enrolment is closed and an open-label extension study is ongoing. This study is registered with EudraCT, 2018-002145-11, and ClinicalTrials.gov, NCT03689972. Findings: Between Dec 26, 2018, and Aug 30, 2019, 605 patients were assessed for eligibility and 499 were enrolled and assigned to receive natalizumab once every 6 weeks (n=251) or once every 4 weeks (n=248). After prespecified adjustments for missing data, mean numbers of new or newly enlarging T2 hyperintense lesions at week 72 were 0·20 (95% CI 0·07–0·63) in the once every 6 weeks group and 0·05 (0·01–0·22) in the once every 4 weeks group (mean lesion ratio 4·24 [95% CI 0·86–20·85]; p=0·076) under the primary estimand, and 0·31 (95% CI 0·12–0·82) and 0·06 (0·01–0·31; mean lesion ratio 4·93 [95% CI 1·05–23·20]; p=0·044) under the secondary estimand. Two participants in the once every 6 weeks group with extreme new or newly enlarging T2 hyperintense lesion numbers (≥25) contributed most of the excess lesions. Adverse events occurred in 194 (78%) of 250 participants in the once every 6 weeks group and 190 (77%) of 247 in the once every 4 weeks group, and serious adverse events occurred in 17 (7%) and 17 (7%), respectively. No deaths were reported. There was one case of asymptomatic progressive multifocal leukoencephalopathy (without clinical signs) in the once every 6 weeks group, and no cases in the once every 4 weeks group; 6 months after diagnosis, the participant was without increased disability and remained classified as asymptomatic. Interpretation: We found a numerical difference in the mean number of new or newly enlarging T2 hyperintense lesions at week 72 between the once every 6 weeks and once every 4 weeks groups, which reached significance under the secondary estimand, but interpretation of statistical differences (or absence thereof) is limited because disease activity in the once every 4 weeks group was lower than expected. The safety profiles of natalizumab once every 6 weeks and once every 4 weeks were similar. Although this trial was not powered to assess differences in risk of progressive multifocal leukoencephalopathy, the occurrence of the (asymptomatic) case underscores the importance of monitoring and risk factor consideration in all patients receiving natalizumab. Funding: Biogen.