Vaccination against influenza and SARS-CoV-2 is recommended in health sciences students to reduce the risk of acquiring these diseases and transmitting them to patients. The aim of the study was to evaluate how the pandemic influenced the modification of influenza vaccination coverage during the 2019/2020 and 2021/2022 campaigns and to analyze the vaccination coverage against SARS-CoV-2 in health sciences students. A cross-sectional study was conducted among students of the Faculty of Nursing, Physiotherapy and Podiatry of the Complutense University of Madrid. A questionnaire was administered in two stages, the first, Q1, before the start of the pandemic, where we analyzed influenza coverage during the 2019/2020 campaign and a second, Q2, 18 months after the start of the pandemic where we analyzed influenza coverage during the 2021/2022 campaign and coverage against SARS-CoV-2. A total of 1894 students (58.78% of the total of those enrolled) participated. Flu vaccination coverage increased from 26.7% in Q1 to 35.0% in Q2 (p < 0.05), being higher in the age group older than 21 years, who studied nursing, were in their fourth year and lived with people at risk. Vaccination coverage against SARS-CoV-2 was very high (97.8%), especially in students vaccinated against influenza. Coverage of the influenza vaccine in health sciences students increased from 2019–2020 to 2021–2022, being higher in the age group older than 21 years, who studied nursing, were in their first and fourth year and lived with people at risk. Coverage of the SARS-CoV-2 vaccine in health sciences students was very high, especially in those vaccinated against influenza.