In situ stress changes at interfaces of ultrathin magnetic films were measured by means of a non-contact optical fiber bundle displacement detector. A bending of the substrate due to stress of a deposited film was detected in cantilever geometry. The highest sensitivity of 134 mV/$mu$m for the displacement detector was realized with a help of computer simulation. The detector was applied to in situ stress measurements of Co/Pt and Ni/Pd magnetic multilayer films prepared on the glass substrates by dc magnetron sputtering. The detector turned out to have a submonolayer sensitivity that enables to observe coherent-to-incoherent transition in these mismatched multilayers and even detect the stress changes within the monoatomic coverage. This highly sensitive detector paves new way to probe the stress relaxation at an interface in ultrathin films.