The mean absolute extinction towards the central parsec of the Milky Way is A_K~3 mag, including both foreground and Galactic center dust. Here we present a measurement of dust extinction within the Galactic old nuclear star cluster (NSC), based on combining differential extinctions of NSC stars with their u_l proper motions along Galactic longitude. Extinction within the NSC preferentially affects stars at its far side, and because the NSC rotates, this causes higher extinctions for NSC stars with negative u_l, as well as an asymmetry in the u_l-histograms. We model these effects using an axisymmetric dynamical model of the NSC in combination with simple models for the dust distribution. Comparing the predicted asymmetry to data for ~7100 stars in several NSC fields, we find that dust associated with the Galactic center mini-spiral with extinction A_K~=0.15-0.8 mag explains most of the data. The largest extinction A_K~=0.8 mag is found in the region of the Western arm of the mini-spiral. Comparing with total A_K determined from stellar colors, we determine the extinction in front of the NSC. Finally, we estimate that for a typical extinction of A_K~=0.4 the statistical parallax of the NSC changes by ~0.4%.