This work develops a computing system consisting of hardware and software, based on a portable prototype for obtaining vital signs data using Internet of Things (IoT) technologies. During the data collection process, the patient is equipped with sensors for body temperature, respiratory rate, and heart rate. The data collected by the sensors is transmitted via wireless connections (Bluetooth and WiFi). The physician views the data using an application designed to run on the Android operating system, or through an HTML page accessible via a configured IP address on the prototype. To evaluate the prototype’s performance, it was used on 20 patients, with 25 records taken per patient over 4 minutes. The results obtained by the prototype are equivalent to those of the conventional methods used by healthcare personnel, showing respiratory rates ranging from 16 to 20 breaths per minute, heart rates from 74 to 76 beats per minute, and body temperatures from 35 °C to 35.8 °C.