Alcohol minimum pricing policies, including minimum unit pricing (MUP), are effective strategies for reducing alcohol consumption and related harm. However, their equity implications remain underexplored. We conducted a rapid review of PubMed and Web of Science, identifying 37 real-world studies assessing the impacts of alcohol minimum pricing. Studies from diverse contexts were synthesised with respect to vulnerable populations and health equity, focusing on consumption, health outcomes, and economic effects. Findings indicate that minimum pricing reduces consumption among people who drink heavily and those in lower socio-economic groups, leading to disproportionate declines in alcohol-related mortality, hospitalisations, and conditions such as liver disease. The greatest health gains occurred among populations experiencing poverty, social marginalization, or alcohol use disorder, highlighting potential to promote health equity. People who drink at low volumes were minimally affected, and substitution effects - such as increased use of non-beverage alcohol or other drugs - were negligible. Purchasing patterns shifted from high-risk, low-cost alcohol products to lower-risk alternatives. Concerns about other unintended consequences, including displacement of essential spending or increased crime, are not strongly supported by current evidence, though isolated findings suggest individuals with severe alcohol use disorder may face challenges. Complementary measures, such as Managed Alcohol Programmes, could mitigate these effects. This review underscores the potential of MUP as a public health strategy that both reduces alcohol-related harm and advances health equity. Further research should examine long-term effects on vulnerable populations and broader outcomes, such as social mobility.