Two-dimensional materials offer exceptional tunability of their properties through strain, electrostatic gating, and related mechanisms. Among these, ZrTe₅ stands out as a material in which band topology can be switched via mechanical deformation. In its bulk form, it lies near a topological phase boundary, allowing efficient modulation of its topological state through strain. While extensive studies exist on bulk ZrTe₅, the topological phase transitions in monolayer and bilayer forms remain largely unexplored. Here we show that monolayer and bilayer ZrTe₅ exhibit distinct strain-induced topological transitions. Mechanical deformation in monolayers can close the topological gap, while bilayers display a richer phase diagram, including topological and trivial insulating phases as well as an intermediate metallic phase. Since thinner van der Waals materials are more amenable to strain tuning, our results identify bilayer ZrTe₅ as a candidate for achieving tunable topological phase transitions using moderate (1-2%) strain as a tuning knob.