Context. Blue straggler stars (BSSs) are observed in Galactic globular clusters and old open clusters. The radial distribution of BSSs has been used to diagnose the dynamical evolution of globular clusters. For the first time, with a reliable sample of BSSs identified with Gaia DR2, we conduct such an analysis for an open cluster. Aims. We aim to identify members, including BSSs, of the oldest known Galactic open cluster Berkeley 17 with the Gaia DR2 proper motions and parallaxes. We study the radial distribution of the BSS population to understand the dynamical evolution of the cluster. Methods. We selected cluster members to populate the colour magnitude diagram in the Gaia filters. Cluster parameters are derived using the brightest members. The BSSs and giant branch stars are identified, and their radial distributions are compared. The segregation of BSSs is also evaluated with respect to the giant branch stars using the minimum spanning tree (MST) analysis. Results. We determine Berkeley 17 to be at 3138.6_−352.9^+285.5 pc. We find 23 BSS cluster members, only two of which were previously identified. We find a bimodal radial distribution of BSSs supported by findings from the MST method. Conclusions. The bimodal radial distribution of BSSs in Berkeley 17 indicates that they have just started to sink towards the cluster centre, placing Berkeley 17 with globular clusters of intermediate dynamical age. This is the first such determination for an open cluster.