Over the past decade, nanosized metal oxides, metals, and bimetallic particles have been actively researched as enzyme mimetic nanomaterials. However, the common issues with individual nanoparticles (NPs) are stabilization, reproducibility, and blocking of active sites by surfactants. These problems promote further studies of composite materials, where NPs are spread on supports, such as graphene derivatives or dichalcogenide nanosheets. Another promising type of support for NPs is the few-layered hexagonal boron nitride (hBN). In this study, we develop surfactant-free nanocomposites containing Pt NPs dispersed on chemically modified hydrophilic hBN nanosheets (hBNNSs). Ascorbic acid was used as a reducing agent for the chemical reduction of the Pt salt in the presence of hBNNS aqueous colloid, resulting in Pt/hBNNS nanocomposites, which were thoroughly characterized with X-ray diffraction, transmission electron microscopy, dynamic light scattering, and X-ray photoelectron and infrared spectroscopies. Similar to graphene oxide binding the metal NPs more efficiently than pure graphene, hydrophilic hBNNSs well stabilize Pt NPs, with particle size down to around 8 nm. We further demonstrate for the first time that Pt/hBNNS nanocomposites exhibit peroxidase-like catalytic activity, accelerating the oxidation of the classical colorless peroxidase substrate 3,3′,5,5′-tetramethylbenzidine (TMB) to its corresponding blue-colored oxidized product in the presence of H2O2. Kinetic and mechanism studies involving terephthalic acid and isopropanol as a fluorescent probe and an •OH radical scavenger, respectively, proved that Pt/hBNNSs assist H2O2 decomposition to active oxygen species (•OH), which are responsible for TMB oxidation. The Pt/hBNNS nanocomposite-assisted oxidation of TMB provides an effective platform for the colorimetric detection of dopamine, an important biomolecule. The presence of increased amounts of dopamine gradually inhibits the catalytic activity of Pt/hBNNSs for the oxidation of TMB by H2O2, thus enabling selective sensing of dopamine down to 0.76 μM, even in the presence of common interfering molecules and on real blood serum samples. The present investigation on Pt/hBNNSs contributes to the knowledge of hBN-based nanocomposites and discovers their new usage as nanomaterials with good enzyme-mimicking activity and dopamine-sensing properties.