We demonstrate a novel method to measure Nth-order (N=1,2,3,4) interferometric autocorrelation with high sensitivity and temporal resolution. It is based on the combination of linear absorption and nonlinear detection in a superconducting nanodetector, providing much higher efficiency than methods based on all-optical nonlinearities. Its temporal resolution is only limited by the quasiparticle energy relaxation time, which is directly measured to be in the 20 ps range for the NbN films used in this work. We present a general model of interferometric autocorrelation with these nonlinear detectors and discuss the comparison with other approaches and possible improvements.