There has been a recent surge in adversarial attacks on deep learning based automatic speech recognition (ASR) systems. These attacks pose new challenges to deep learning security and have raised significant concerns in deploying ASR systems in safety-critical applications. In this work, we introduce WaveGuard: a framework for detecting adversarial inputs that are crafted to attack ASR systems. Our framework incorporates audio transformation functions and analyses the ASR transcriptions of the original and transformed audio to detect adversarial inputs. We demonstrate that our defense framework is able to reliably detect adversarial examples constructed by four recent audio adversarial attacks, with a variety of audio transformation functions. With careful regard for best practices in defense evaluations, we analyze our proposed defense and its strength to withstand adaptive and robust attacks in the audio domain. We empirically demonstrate that audio transformations that recover audio from perceptually informed representations can lead to a strong defense that is robust against an adaptive adversary even in a complete white-box setting. Furthermore, WaveGuard can be used out-of-the box and integrated directly with any ASR model to efficiently detect audio adversarial examples, without the need for model retraining.