BACKGROUND: Secondary distribution of HIV self-testing (HIVST) kits by patients attending clinic services to their partners could improve the rate of HIV diagnosis. We aimed to investigate whether secondary administration of HIVST kits, with or without an additional financial incentive, via women receiving antenatal care (ANC) or via people newly diagnosed with HIV (ie, index patients) could improve the proportion of male partners tested or the number of people newly diagnosed with HIV. METHODS: We did a three-arm, open-label, pragmatic, cluster-randomised trial of 27 health centres (clusters), eligible if they were a government primary health centre providing ANC, HIV testing, and ART services, across four districts of Malawi. We recruited women (aged ≥18 years) attending their first ANC visit and whose male partner was available, not already taking ART, and not already tested for HIV during this pregnancy (ANC cohort), and people (aged ≥18 years) with newly diagnosed HIV during routine clinic HIV testing who had at least one sexual contact not already known to be HIV-positive (index cohort). Centres were randomly assigned (1:1:1), using a public selection of computer-generated random allocations, to enhanced standard of care (including an invitation for partners to attend HIV testing services), HIVST only, or HIVST plus a US$10 financial incentive for retesting. The primary outcome for the ANC cohort was the proportion of male partners reportedly tested, as ascertained by interview with women in this cohort at day 28. The primary outcome for the index cohort was the geometric mean number of new HIV-positive people identified per facility within 28 days of enrolment, as measured by observed HIV test results. Cluster-level summaries compared intervention with standard of care by intention to treat. This trial is registered with ClinicalTrials.gov, NCT03705611. FINDINGS: Between Sept 8, 2018, and May 2, 2019, nine clusters were assigned to each trial arm, resulting in 4544 eligible women in the ANC cohort (1447 [31·8%] in the standard care group, 1465 [32·2%] in the HIVST only group, and 1632 [35·9%] in HIVST plus financial incentive group) and 708 eligible patients in the index cohort (234 [33·1%] in the standard care group, 169 [23·9%] in the HIVST only group, and 305 [42·9%] in the HIVST plus financial incentive group). 4461 (98·2%) of 4544 eligible women in the ANC cohort and 645 (91·1%) of 708 eligible patients in the index cohort were recruited, of whom 3378 (75·7%) in the ANC cohort and 439 (68·1%) in the index cohort were interviewed after 28 days. In the ANC cohort, the mean proportion of reported partner testing per cluster was 35·0% (SD 10·0) in the standard care group, 73·0% in HIVST only group (13·1, adjusted risk ratio [RR] 1·71, 95% CI 1·48-1·98; p<0·0001), and 65·2% in the HIVST plus financial incentive group (11·6, adjusted RR 1·62, 1·45-1·81; p<0·0001). In the index cohort, the geometric mean number of new HIV-positive sexual partners per cluster was 1·35 (SD 1·62) for the standard care group, 1·91 (1·78) for the HIVST only group (incidence rate ratio adjusted for number eligible as an offset in the negative binomial model 1·65, 95% CI 0·49-5·55; p=0·3370), and 3·20 (3·81) for the HIVST plus financial incentive group (3·11, 0·99-9·77; p=0·0440). Four self-resolving, temporary marital separations occurred due to disagreement in couples regarding HIV self-test kits. INTERPRETATION: Although administration of HIVST kits in the ANC cohort, even when offered alongside a financial incentive, did not identify significantly more male patients with HIV than did standard care, out-of-clinic options for HIV testing appear more acceptable to many male partners of women with HIV, increasing test uptake. Viewed in the current context, this approach might allow continuation of services despite COVID-19-related lockdowns. FUNDING: Unitaid, through the Self-Testing Africa Initiative.