Balancing the risk of bleeding and thrombosis after acute myocardial infarction (AMI) is challenging, and the optimal antithrombotic therapy remains uncertain. The potential of non-vitamin K antagonist oral anticoagulants (NOACs) to prevent ischaemic cardiovascular events is promising, but the evidence remains limited. To evaluate the efficacy and safety of non-vitamin-K-antagonist oral anticoagulants (NOACs) in addition to background antiplatelet therapy, compared with placebo, antiplatelet therapy, or both, after acute myocardial infarction (AMI) in people without an indication for anticoagulation (i.e. atrial fibrillation or venous thromboembolism). We searched CENTRAL, MEDLINE, Embase, the Conference Proceedings Citation Index - Science, and two clinical trial registers in September 2022 with no language restrictions. We checked the reference lists of included studies for any additional trials. We searched for randomised controlled trials (RCTs) that evaluated NOACs plus antiplatelet therapy versus placebo, antiplatelet therapy, or both, in people without an indication for anticoagulation after an AMI. Two review authors independently checked the results of searches to identify relevant studies, assessed each included study, and extracted study data. We conducted random-effects pairwise analyses using Review Manager Web, and network meta-analysis using the R package 'netmeta'. We ranked competing treatments by P scores, which are derived from the P values of all pairwise comparisons and allow ranking of treatments on a continuous 0-to-1 scale. We identified seven eligible RCTs, including an ongoing trial that we could not include in the analysis. Of the six RCTs involving 33,039 participants, three RCTs compared rivaroxaban with placebo, two RCTs compared apixaban with placebo, and one RCT compared dabigatran with placebo. All participants in the six RCTs received concomitant antiplatelet therapy. The available evidence suggests that rivaroxaban compared with placebo reduces the rate of all-cause mortality (risk ratio (RR) 0.82, 95% confidence interval (CI) 0.69 to 0.98; number needed to treat for an additional beneficial outcome (NNTB) 250; 3 studies, 21,870 participants; high certainty) and probably reduces cardiovascular mortality (RR 0.83, 95% CI 0.69 to 1.01; NNTB 250; 3 studies, 21,870 participants; moderate certainty). There is probably little or no difference between apixaban and placebo in all-cause mortality (RR 1.09, 95% CI 0.88 to 1.35; number needed to treat for an additional harmful outcome (NNTH) 334; 2 studies, 8638 participants; moderate certainty) and cardiovascular mortality (RR 0.99, 95% CI 0.77 to 1.27; number needed to treat not applicable; 2 studies, 8638 participants; moderate certainty). Dabigatran may reduce the rate of all-cause mortality compared with placebo (RR 0.57, 95% CI 0.31 to 1.06; NNTB 63; 1 study, 1861 participants; low certainty). Dabigatran compared with placebo may have little or no effect on cardiovascular mortality, although the point estimate suggests benefit (RR 0.72, 95% CI 0.34 to 1.52; NNTB 143; 1 study, 1861 participants; low certainty). Two of the investigated NOACs were associated with an increased risk of major bleeding compared to placebo: apixaban (RR 2.41, 95% CI 1.44 to 4.06; NNTH 143; 2 studies, 8544 participants; high certainty) and rivaroxaban (RR 3.31, 95% CI 1.12 to 9.77; NNTH 125; 3 studies, 21,870 participants; high certainty). There may be little or no difference between dabigatran and placebo in the risk of major bleeding (RR 1.74, 95% CI 0.22 to 14.12; NNTH 500; 1 study, 1861 participants; low certainty). The results of the network meta-analysis were inconclusive between the different NOACs at all individual doses for all primary outcomes. However, low-certainty evidence suggests that apixaban (combined dose) may be less effective than rivaroxaban and dabigatran for preventing all-cause mortality after AMI in people without an indication for anticoagulation. Compared with placebo, rivaroxaban reduces all-cause mortality and probably reduces cardiovascular mortality after AMI in people without an indication for anticoagulation. Dabigatran may reduce the rate of all-cause mortality and may have little or no effect on cardiovascular mortality. There is probably no meaningful difference in the rate of all-cause mortality and cardiovascular mortality between apixaban and placebo. Moreover, we found no meaningful benefit in efficacy outcomes for specific therapy doses of any investigated NOACs following AMI in people without an indication for anticoagulation. Evidence from the included studies suggests that rivaroxaban and apixaban increase the risk of major bleeding compared with placebo. There may be little or no difference between dabigatran and placebo in the risk of major bleeding. Network meta-analysis did not show any superiority of one NOAC over another for our prespecified primary outcomes. Although the evidence suggests that NOACs reduce mortality, the effect size or impact is small; moreover, NOACs may increase major bleeding. Head-to-head trials, comparing NOACs against each other, are required to provide more solid evidence.