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The layered oxide Na₂Ni₂TeO₆ (P2 type) has a hexagonal crystal structure (P6₃/mcm space group) that contains Ni²⁺ honeycomb layers intercalated with Na ions. The Ni lattice could be studied from the perspective of Kitaev magnetism, while the sodium ions exhibit high ionic conductivity. Ni²⁺ moments in Na₂Ni₂TeO₆ are known to adopt a quasi-two-dimensional zig-zag arrangement. The magnetic response of Na₂Ni₂TeO₆ in bulk measurements showed a robust magnetic lattice which was not influenced by external magnetic fields upto 8 T. In this study we investigate the effects of diluting the Ni lattice in Na₂Ni₂TeO_6, focusing on the four compounds, Na₂(Ni_2-xMg_x)TeO₆ (x = 0.10, 0.15, 0.20, 0.25). Using magnetic susceptibility, specific heat and neutron diffraction, we map out the magnetic phase diagram of this solid solution. The magnetic phase transition temperature of the parent compound (x = 0; 27 K) is found to decrease slightly to 25 K with Mg dilution. Even with 5% substitution, a new low-temperature anomaly in magnetic susceptibility emerges. Our neutron diffraction analysis shows that the long-range magnetic order in x = 0 case is destabilized to short-range order even with 5% Mg in the Ni lattice.