The microstructure of Ti6Al4V alloy, manufactured using laser powder bed fusion (L-PBF), is affected by process parameters and heat treatment. However, their influence on the nano-mechanical behavior of this widely applicable alloy is still unknown and scarcely reported. This study aims to investigate the influence of the frequently used annealing heat treatment on mechanical properties, strain-rate sensitivity, and creep behavior of L-PBF Ti6Al4V alloy. Furthermore, the influence of different utilized L-PBF laser power–scanning speed combinations on mechanical properties of annealed specimens has been studied as well. It has been found that the effect of high laser power remains present in the microstructure even after annealing, resulting in increase in nano-hardness. Moreover, the linear relation between the Young’s modulus and the nano-hardness after annealing has been established. Thorough creep analysis revealed dislocation motion as a dominant deformation mechanism, both for as-built and annealed conditions of the specimens. Although annealing heat treatment is beneficial and widely recommended, it reduces the creep resistance of Ti6Al4V alloy manufactured using L-PBF. The results presented within this research article contribute to the L-PBF process parameter selection, as well as to understanding the creep behavior of these novel and widely applicable materials.