Climate change is rapidly reshaping oceanographic conditions, expanding ecological windows for marine invasive species (MIS) through warming, altered circulation, acidification, and deoxygenation. These shifts are amplifying invasion pressure across biogeographic boundaries, destabilizing native ecosystems and threatening fisheries, coastal protection, and blue carbon storage. Here, we synthesize evidence across four domains such as climate drivers, invasion pathways, ecological impacts, and governance responses to evaluate how climate change is fundamentally altering marine invasion dynamics. This review identifies three critical global gaps: (i) the absence of climate-integrated biosecurity metrics capable of anticipating future invasion risk, (ii) limited early-warning thresholds linking environmental change to invasion probability, and (iii) weak regional coordination across shared marine pathways, particularly in semi-enclosed seas and climate-sensitive regions. Despite growing policy attention, most existing biosecurity frameworks remain static and reactive, poorly aligned with accelerating climate variability. To address these gaps, we propose a climate-smart marine biosecurity framework that integrates molecular surveillance (e.g., eDNA), dynamic risk modeling, and predictive monitoring aligned with Sustainable Development Goals and emerging global biodiversity targets. By reframing MIS management as a core component of climate adaptation rather than a standalone conservation issue, this review provides an operational pathway to shift biosecurity from post-invasion response toward anticipatory, climate-informed prevention. The urgency of this transition is underscored by the rapid emergence of new invasion corridors and the narrowing window for effective intervention in a warming ocean.