Generalization is a pivotal challenge for agents following natural language instructions. To approach this goal, we leverage a vision-language model (VLM) for visual grounding and transfer its vision-language knowledge into reinforcement learning (RL) for object-centric tasks, which makes the agent capable of zero-shot generalization to unseen objects and instructions. By visual grounding, we obtain an object-grounded confidence map for the target object indicated in the instruction. Based on this map, we introduce two routes to transfer VLM knowledge into RL. Firstly, we propose an object-grounded intrinsic reward function derived from the confidence map to more effectively guide the agent towards the target object. Secondly, the confidence map offers a more unified, accessible task representation for the agent's policy, compared to language embeddings. This enables the agent to process unseen objects and instructions through comprehensible visual confidence maps, facilitating zero-shot object-level generalization. Single-task experiments prove that our intrinsic reward significantly improves performance on challenging skill learning. In multi-task experiments, through testing on tasks beyond the training set, we show that the agent, when provided with the confidence map as the task representation, possesses better generalization capabilities than language-based conditioning.