In past years the IceCube Collaboration has reported the observation of astrophysical high-energy neutrino events in several analyses. Despite compelling evidence for the first identification of a neutrino source, TXS 0506+056, the origin of the majority of these events is still unknown. In this paper, we search for a possible transient origin of the IceCube astrophysical events using neutrino events detected by the ANTARES telescope. The arrival time and direction of 6894 track-like and 160 shower-like events detected over 2346 days of livetime are examined to search for coincidences with 54 IceCube high-energy track-like neutrino events, by means of a maximum likelihood method. No significant correlation is observed and upper limits on the one-flavor neutrino fluence from the direction of the IceCube candidates are derived. The nonobservation of time and space correlation within the time window of 0.1 days with the two most energetic IceCube events constrains the spectral index of a possible point-like transient neutrino source to be harder than −2.3 and −2.4 for each event, respectively.