Controlling text-to-speech (TTS) systems to synthesize speech with the prosodic characteristics expected by users has attracted much attention. To achieve controllability, current studies focus on two main directions: (1) using reference speech as prosody prompt to guide speech synthesis, and (2) using natural language descriptions to control the generation process. However, finding reference speech that exactly contains the prosody that users want to synthesize takes a lot of effort. Description-based guidance in TTS systems can only determine the overall prosody, which has difficulty in achieving fine-grained prosody control over the synthesized speech. In this paper, we propose DrawSpeech, a sketch-conditioned diffusion model capable of generating speech based on any prosody sketches drawn by users. Specifically, the prosody sketches are fed to DrawSpeech to provide a rough indication of the expected prosody trends. DrawSpeech then recovers the detailed pitch and energy contours based on the coarse sketches and synthesizes the desired speech. Experimental results show that DrawSpeech can generate speech with a wide variety of prosody and can precisely control the fine-grained prosody in a user-friendly manner. Our implementation and audio samples are publicly available.