In this paper, a nonlinear integro-dynamic equation on time scales with local initial condition is considered. The purpose of this paper is to prove existence and uniqueness of solutions and to investigate qualitative properties of solutions of this equation such as boundedness, dependence of solutions on initial conditions, functions, and parameters, and Ulam stability. The analysis is based on the Krasnoselskiĭ fixed point theorem and Gronwall-type dynamic inequalities. For the illustrative purpose of our main results, examples on a nonstandard time scale domain are provided.