MXenes, a recently developed class of 2D materials, have attracted considerable attention because of their graphene-like but highly tunable properties. It appears that the metallic properties of MXene titanium carbide are pronounced in near-infrared with well-defined localised surface plasmon resonance (LSPR). Here, we report on a curved photonic nanojet, known as the photonic hook, applied on a titanium carbide nanoparticle for the particle's optomechanical manipulation. We show that the optical forces generated and applied on titanium carbide nanoparticles of various shapes are based on the LSPR excitation in near-infrared. We compare the obtained results to traditional plasmonic gold nanoparticles which exhibit LSPR in visible. Considering the diversity of the MXene family, this study is a first step towards photonic devices that utilize optomechanical manipulation in near-infrared for biomedical research, optical trapping and others.