In this work, we prove a small-time central limit theorem for the finite-dimensional distributions of solutions to stochastic Volterra integral equations as well as its extension to a functional CLT, where we focus on coefficients satisfying linear growth and Hölder conditions. As we consider the (potentially singular) Riemann-Liouville kernel, the Hurst parameter H > 0 plays an essential role in choosing the appropriate normalizing sequence for the CLT. As a consequence, we obtain also the small-time asymptotics for prices of at-the-money digital calls in market models with sufficient trading limitations. Finally, we prove the absolute continuity of the solution with respect to the Lebesgue measure under the additional assumption that the diffusion coefficient does not attain zero. Provided that the densities are sufficiently regular in time and in combination with the above CLT, we can, moreover, show the non-Markovianity of the process, which is of importance for applications in mathematical finance as it highlights the need for more sophisticated concepts for pricing and hedging financial derivatives.