We study the formation of (quasi-) coherent matter waves emerging from a Mott insulator for strongly interacting bosons on a one-dimensional lattice. It has been shown previously that a quasi- condensate emerges at momentum k(cond) = pi/2a, where a is the lattice constant, in the limit of infinitely strong repulsion (hard-core bosons). Here, we show that this phenomenon persists for all values of the repulsive interaction that lead to a Mott insulator at a commensurate filling. The non-equilibrium dynamics of hard-core bosons is treated exactly by means of a Jordan - Wigner transformation, and the generic case is studied using a time-dependent density matrix renormalization group technique. Different methods for controlling the emerging matter wave are discussed.