Recently, many companies have been providing the capabilities of large language models as services. These Language-Model-as-a-Service (LMaaS) offerings support a variety of user tasks through in-context learning from prompts, which include instructions and demonstrations of the task. However, for users, manually crafting prompts or running automatic prompt tuning methods themselves can be demanding. Despite these challenges, LMaaS providers do not offer automatic prompt engineering methods as part of their services. One of the major obstacles to deploying them on an LMaaS is the heavy computational costs associated with automatic prompt engineering methods. These methods are typically designed to iterate through tens of thousands of examples, which impose unaffordable overheads for LMaaS providers. In this paper, we introduce MetaL-Prompt, a novel lightweight automatic prompt generation method for LMaaS. MetaL-Prompt meta-trains a prompt generation model (PGM) to enable robust learning by the language model from the contexts created by the generated prompts (i.e., in-context learning). Thanks to our meta-learning approach, a PGM can generate prompts for unseen tasks without requiring additional training for those specific tasks. Furthermore, the PGM can generate prompts with a single forward pass, significantly reducing computational costs compared to previous methods. We evaluate MetaL-Prompt on a range of unseen tasks and find that it improves performance by up to 19.4% in terms of mean F1 score on QA datasets compared to the state-of-the-art baseline P-tuning, with limited computational cost.