Prescribed burns help reduce wildfire risk, yet assessing post-burn vegetation recovery remains difficult due to the high dimensionality and labeling cost of hyperspectral imagery (HSI). We propose BurnSSL-DRL, a label-efficient framework that couples self-supervised learning (SSL) with deep reinforcement learning (DRL) for spectral band selection and vegetation classification. The DRL agent prioritized low-wavelength VNIR regions linked to chlorophyll degradation and soil exposure, reducing dimensionality to 30 bands while retaining key information. When combined with a 3D spectral–spatial CNN and class-balancing strategies (SMOTE + weighted loss), the BurnSSL-DRL achieved a macro-F1 ≈ 0.52—about 4–6% higher than PCA and mRMR baselines—and improved minority-class F1 (Grass 0.02 → 0.30, Soil 0.40 → 0.65). These results demonstrate that BurnSSL-DRL enables compact, interpretable, and accurate post-burn vegetation mapping, supporting scalable and near-real-time ecological monitoring from UAV platforms.