Existing multimodal audio generation models often lack precise user control, which limits their applicability in professional Foley workflows. In particular, these models focus on the entire video and do not provide precise methods for prioritizing a specific object within a scene, generating unnecessary background sounds, or focusing on the wrong objects. To address this gap, we introduce the novel task of video object segmentation-aware audio generation, which explicitly conditions sound synthesis on object-level segmentation maps. We present SAGANet, a new multimodal generative model that enables controllable audio generation by leveraging visual segmentation masks along with video and textual cues. Our model provides users with fine-grained and visually localized control over audio generation. To support this task and further research on segmentation-aware Foley, we propose Segmented Music Solos, a benchmark dataset of musical instrument performance videos with segmentation information. Our method demonstrates substantial improvements over current state-of-the-art methods and sets a new standard for controllable, high-fidelity Foley synthesis. Code, samples, and Segmented Music Solos are available at https://saganet.notion.site