Accurate segmentation of 3D medical images such as MRI and CT is essential for clinical diagnosis and treatment planning. Foundation models like the Segment Anything Model (SAM) provide powerful general-purpose representations but struggle in medical imaging due to domain shift, their inherently 2D design, and the high computational cost of fine-tuning. To address these challenges, we propose Mamba-SAM, a novel and efficient hybrid architecture that combines a frozen SAM encoder with the linear-time efficiency and long-range modeling capabilities of Mamba-based State Space Models (SSMs). We investigate two parameter-efficient adaptation strategies. The first is a dual-branch architecture that explicitly fuses general features from a frozen SAM encoder with domain-specific representations learned by a trainable VMamba encoder using cross-attention. The second is an adapter-based approach that injects lightweight, 3D-aware Tri-Plane Mamba (TPMamba) modules into the frozen SAM ViT encoder to implicitly model volumetric context. Within this framework, we introduce Multi-Frequency Gated Convolution (MFGC), which enhances feature representation by jointly analyzing spatial and frequency-domain information via 3D discrete cosine transforms and adaptive gating. Extensive experiments on the ACDC cardiac MRI dataset demonstrate the effectiveness of the proposed methods. The dual-branch Mamba-SAM-Base model achieves a mean Dice score of 0.906, comparable to UNet++ (0.907), while outperforming all baselines on Myocardium (0.910) and Left Ventricle (0.971) segmentation. The adapter-based TP MFGC variant offers superior inference speed (4.77 FPS) with strong accuracy (0.880 Dice). These results show that hybridizing foundation models with efficient SSM-based architectures provides a practical and effective solution for 3D medical image segmentation.