Earthquake triggering data exhibit long-range spatio-temporal correlations of the power-law form C(l) ~ l-α and anomalously-slow temporal diffusion of the mean triggering distance of the form: $langle$l$rangle$ ~ tH, with H < 0.5. We examine spatio-temporal correlations in subsurface effective stress state caused by fluid injection and extraction at well sites in a hydrocarbon reservoir using a multivariate statistical regression model, and observe long-range correlations in flow rate that cannot be caused by Darcy flow alone. Significantly-correlated well pairs align with the directions of incipient horizontal-displacement tensile and shear failure in the present-day stress field, while the contours of the first principal component of the regression matrix closely follow the macroscopic fault pattern in the main producing horizon. The correlation function for well pairs has a power-law form with α ≈ 0.5, and the mean correlation distance increases with H ≈ 0.33, implying a similar critical-point response to perturbations in effective stress as the earthquake data.