No. Vaccines prepare the immune system to fight the virus. Billions of doses of COVID-19 vaccines have been administered worldwide and they have shown to be very effective in preventing severe COVID-19 disease. If COVID-19 vaccines weakened the immune system people who are vaccinated against COVID-19 would have more severe disease. This is not the case.
In the European Region, a recent study has shown that about 500,000 lives have been saved through vaccination among adults over 60 in 33 countries. The vast majority of people requiring intensive care in hospitals for COVID-19 have been unvaccinated.