Single-molecule measurements of biomolecules can provide information about the molecular interactions and kinetics that are hidden in ensemble measurements. However, there is a requirement for techniques with improved sensitivity and time resolution for use in exploring biomolecular systems with fast dynamics. Here, we report the detection of DNA hybridization at the single-molecule level using a carbon nanotube field-effect transistor. By covalently attaching a single-stranded probe DNA sequence to a point defect in a carbon nanotube, we are able to measure two-level fluctuations in the conductance of the nanotube in the presence of a complementary DNA target. The kinetics of the system are studied as a function of temperature, allowing the measurement of rate constants, melting curves and activation energies for different sequences and target concentrations. The kinetics demonstrate non-Arrhenius behaviour, in agreement with DNA hybridization experiments using fluorescence correlation spectroscopy. This technique is label-free and could be used to probe single-molecule dynamics at microsecond timescales.