Multimodal Relation Extraction is crucial for constructing flexible and realistic knowledge graphs. Recent studies focus on extracting the relation type with entity pairs present in different modalities, such as one entity in the text and another in the image. However, existing approaches require entities and objects given beforehand, which is costly and impractical. To address the limitation, we propose a novel task, Multimodal Entity-Object Relational Triple Extraction, which aims to extract all triples (entity span, relation, object region) from image-text pairs. To facilitate this study, we modified a multimodal relation extraction dataset MORE, which includes 21 relation types, to create a new dataset containing 20,264 triples, averaging 5.75 triples per image-text pair. Moreover, we propose QEOT, a query-based model with a selective attention mechanism, to dynamically explore the interaction and fusion of textual and visual information. In particular, the proposed method can simultaneously accomplish entity extraction, relation classification, and object detection with a set of queries. Our method is suitable for downstream applications and reduces error accumulation due to the pipeline-style approaches. Extensive experimental results demonstrate that our proposed method outperforms the existing baselines by 8.06% and achieves state-of-the-art performance.