Connected medical devices are already paving the way towards the realization of Smart Hospitals where patient care is improved thanks to Internet of Things (IoT) solutions. Following this trend, in this paper we propose an IoT cloud-based network for anesthesia on-line monitoring. This architecture allows the anesthesiologist to remain simultaneously connected to all the sedated patients through an Android app. Moreover, medical data from the patients can be shared on a cloud solution accessible by a web application enabling teleconsulting. Hence, by accessing the cloud, medical specialists can consult the shared data from everywhere and at any time. The flexibility and the portability of our monitoring architecture ensure the possibility to interface with any medical device which can wirelessly send the measured data. Therefore, other medical monitoring applications can also be addressed.