The results of observations of the gravitational-wave (GW) event S190425z recorded by the LIGO/Virgo detectors with the anti-coincidence shield (ACS) of the SPI gamma-ray spectrometer onboard the INTEGRAL observatory are presented. With a high probability (>99%) it was associated with a neutron star (NS) merger in a close binary system. This is only the second event of such a type in the history of gravitational-wave observations (after GW170817). A weak gamma-ray burst, GRB190425, consisting of two pulses ～0.5 and ～5.9 s after the NS merger in the event S190425z with an a priori significance of 3.5 and 4.4σ (taken together 5.5σ) was detected by SPI-ACS. Analysis of the SPI-ACS count rate history recorded on these days (a total of ～125 ks of observations) has shown that the rate of random occurrence of two close spikes with the characteristics of GRB190425 does not exceed 6.4 × 10^?5 s^?1 (i.e., such events occur by chance, on average, every ～4.3 hours). Note that the time profile of GRB190425 has much in common with the profile of GRB170817A accompanying the event GW170817, that both NS mergers were the nearest (≤150 Mpc) of all the events recorded by the LIGO/Virgo detectors, and that no significant excesses of the gamma-ray flux above the background were detected in any of ～30 black hole merger events recorded to date by these detectors. No bursts of hard radiation were detected in the field of view of the SPI and IBIS/ISGRI gamma-ray telescopes onboard INTEGRAL. This, along with the absence of detection of gamma-ray emission from GRB190425 by the GBM gamma-ray burst monitor of the Fermi observatory suggesting its occultation by the Earth, allows the localization region for the source of this GWevent to be reduced significantly. The parameters E_iso and E_p for GRB190425 are estimated and compared with those for GRB170817A.