Context. Transient neutrino sources such as gamma-ray bursts (GRBs) and supernovae (SNe) are hypothesized to emit bursts of high-energy neutrinos on a time-scale of ≲ 100 s. While GRB neutrinos would be produced in high relativistic jets, core-collapse SNe might host soft-relativistic jets, which become stalled in the outer layers of the progenitor star leading to an efficient production of high-energy neutrinos. Aims. To increase the sensitivity to these neutrinos and identify their sources, a low-threshold optical follow-up program for neutrino multiplets detected with the IceCube observatory has been implemented. Methods. If a neutrino multiplet, i.e. two or more neutrinos from the same direction within 100 s, is found by IceCube a trigger is sent to the Robotic Optical Transient Search Experiment, ROTSE. The 4 ROTSE telescopes immediately start an observation program of the corresponding region of the sky in order to detect an optical counterpart to the neutrino events. Results. No statistically significant excess in the rate of neutrino multiplets has been observed and furthermore no coincidence with an optical counterpart was found. Conclusions. The search allows, for the first time, to set stringent limits on current models predicting a high-energy neutrino flux from soft relativistic hadronic jets in core-collapse SNe. We conclude that a sub-population of SNe with typical Lorentz boost factor and jet energy of 10 and 3 × 1051 erg, respectively, does not exceed 4.2% at 90% confidence. © 2012 ESO.