The relationship between sustainable growth and public investment, considered one of the key factors, is a topic of interest in the context of globally adopted sustainable development strategies and current budgetary constraints, especially in the case of tight budgets in developing countries, which constrain public investment more than current expenditure, for political or other reasons. Although there are endogenous growth patterns that incorporate public spending as a factor that promotes growth, the findings in the empirical literature provide contradictory results. The study is an empirical investigation into the effects of public investment on sustainable economic growth in emerging EU and Central European countries. For the period 1995–2019, the research shows that, in most of the countries included in the sample, the long-term impact of a public capital shock on GDP is estimated to be negative. The analysis of the effect of public investment on sustainable economic growth was performed by applying the VAR model and impulse response functions, the results being confirmed by estimating the accumulated multiplier to obtain the GDP response to a shock equal to a standard deviation of public capital.