Aspect-Based Sentiment Analysis (ABSA) identifies sentiments toward specific aspects of an entity. While progress has been substantial for high-resource languages such as English, low-resource languages like Bangla remain underexplored due to limited annotated data and linguistic challenges. We propose Gen-mABSA-T5, a multilingual zero-shot generative framework for ABSA based on Flan-T5, incorporating prompt engineering and Natural Language Inference (NLI). Without task-specific training, Gen-mABSA-T5 achieves state-of-the-art zero-shot accuracy of 61.56% on the large Bangla corpus, 73.50% on SemEval Laptop, and 73.56% on SemEval Restaurant outperforming both English and Bangla task-specific models in zero-shot settings. It delivers reasonable performance against very large general-purpose models on both English and Bangla benchmarks. These results highlight the effectiveness of generative, zero-shot approaches for ABSA in low-resource and multilingual settings.