Background: Energy drinks (EDs) are very popular among young people, who consume them for various reasons. A standard ED typically contains 80 mg of caffeine, as well as glucose, taurine, vitamins and other ingredients. Excessive consumption of EDs and accumulation of the above ingredients, as well as their mutual interactions, can be hazardous to the health of young adults. The purpose of this study was to assess the effect of acute consumption of energy drinks on blood pressure, heart rate and blood glucose. Methods: The study involved 68 volunteers, healthy young adults (mean age 25 years), who were divided into two groups: the first consumed three EDs at one-hour intervals, and the second drank the same amount of water. All participants had their blood pressure (BP)—systolic and diastolic (SBP and DBP)—as well as heart rate (HR) and blood glucose (BG) measured. In addition, participants could report any health problems before and after consuming each portion of ED. Results: In the above experiment, having consumed three portions of ED (240 mg of caffeine), the participants presented a significant increase in DBP (p = 0.003), by over 8%, which coincided with a lack of any significant impact on SBP (p = 0.809). No significant changes were noted in HR (p = 0.750). Consumption of EDs caused a significant increase (p < 0.001) in BG, by ca. 21%, on average. Some participants reported various discomforts, which escalated after 2 and 3 EDs. Conclusions: Acute consumption of EDs contributed to increased diastolic blood pressure, blood glucose and level of discomfort in healthy young people. Our results reinforce the need for further studies on a larger population to provide sufficient evidence.