Sleep is known to be a key factor in emotional regulation and overall mental health. In this study, we explore the integration of sleep measures from the previous night into wearable-based mood recognition. To this end, we propose NapTune, a novel prompt-tuning framework that utilizes sleep-related measures as additional inputs to a frozen pre-trained wearable time-series encoder by adding and training lightweight prompt parameters to each Transformer layer. Through rigorous empirical evaluation, we demonstrate that the inclusion of sleep data using NapTune not only improves mood recognition performance across different wearable time-series namely ECG, PPG, and EDA, but also makes it more sample-efficient. Our method demonstrates significant improvements over the best baselines and unimodal variants. Furthermore, we analyze the impact of adding sleep-related measures on recognizing different moods as well as the influence of individual sleep-related measures.