Generating speech from a face image is crucial for developing virtual humans capable of interacting using their unique voices, without relying on pre-recorded human speech. In this paper, we propose Face-StyleSpeech, a zero-shot Text-To-Speech (TTS) synthesis model that generates natural speech conditioned on a face image rather than reference speech. We hypothesize that learning entire prosodic features from a face image poses a significant challenge. To address this, our TTS model incorporates both face and prosody encoders. The prosody encoder is specifically designed to model speech style characteristics that are not fully captured by the face image, allowing the face encoder to focus on extracting speaker-specific features such as timbre. Experimental results demonstrate that Face-StyleSpeech effectively generates more natural speech from a face image than baselines, even for unseen faces. Samples are available on our demo page.