We analyze the inter event time distribution of fluid-injection-induced earthquakes for six catalogs collected at geothermal injection sites at Soultz-sous-Forêts and Basel. We find that the distribution of waiting times during phases of constant seismicity rate coincides with the exponential distribution of the homogeneous Poisson process (HPP). We analyze the waiting times for the complete event catalogs and find that, as for naturally occurring earthquakes, injection induced earthquakes are distributed according to a non homogeneous Poisson process in time. Moreover, the process of event occurrence in the injection volume domain is a HPP. These results indicate that fluid-injection-induced earthquakes are directly triggered by the loading induced by the fluid injection. We also consider the spatial distance between events and perform a nearest neighbor analysis in the time-space-magnitude domain. Our analysis including a comparison to a synthetic catalog created according to the ETAS model reveals no signs of causal relationships between events. Therefore, coupling effects between events are very weak. The Poisson model seems to be a very good approximation of fluid induced seismicity.