The structure of K2Ni2(MoO4)3 consists of S=1 tetramers formed by Ni2+ ions. The magnetic susceptibility χ(T) and specific heat CP(T) data on a single crystal show a broad maximum due to the low dimensionality of the system with short-range spin correlations. A sharp peak is seen in χ(T) and CP(T) at about 1.13 K, well below the broad maximum. This is an indication of magnetic long-range order, i.e., the absence of spin gap in the ground state. Interestingly, the application of a small magnetic field (H>0.1 T) induces magnetic behavior akin to the Bose-Einstein condensation (BEC) of triplon excitations observed in some spin-gap materials. Our results demonstrate that the temperature-field (T-H) phase boundary follows a power law (T-TN) 1/α with the exponent 1/α close to 23, as predicted for the BEC scenario. The observation of BEC of triplon excitations in small H infers that K2Ni2(MoO4)3 is located in the proximity of a quantum critical point, which separates the magnetically ordered and spin-gap regions of the phase diagram. © 2017 American Physical Society.