Hybrid simulation is essential for modeling biochemical systems that mix low-copy stochastic dynamics with high-abundance deterministic processes. We present HySimODE, a Python framework that automates hybrid simulation directly from user-defined ordinary differential equation-based models. HySimODE uses a short deterministic pre-simulation and a machine-learning classifier to automatically assign each species to a stochastic or deterministic regime, and then combines a simple stochastic update rule with a stiff ODE solver in a single simulation loop. The classifier was trained and validated on a diverse dataset of biochemical ODE models spanning multiple dynamical regimes, enabling robust stochastic-deterministic partitioning beyond simple abundance thresholds. This design eliminates manual specification of regimes, avoids model reformulation, and enables reproducible, data-driven hybrid simulations of ODE-only biochemical models, including systems with saturable kinetics, effective-rate laws, or macro-energetic variables that lack a consistent reaction-network representation. Benchmarking against deterministic integrators, stochastic simulations, and abundance-threshold hybrid approaches demonstrates that HySimODE provides a practical and scalable framework for hybrid simulation of ODE-defined biochemical systems. We demonstrate its utility on two distinct case studies: a host-circuit interaction model from synthetic biology and a long-term synaptic potentiation model from neurobiology. HySimODE includes a modular adapter system that automatically converts ODE models written in concentrations into molecular counts, enabling universal compatibility across biochemical systems without code modification.