Unlike classical software, where logging and runtime tracing can effectively reveal internal execution status, quantum circuits possess unique properties, such as the no-cloning theorem and measurement-induced collapse, that prevent direct observation or duplication of their states. These characteristics make it especially challenging to monitor the execution of quantum circuits, complicating essential tasks such as debugging and runtime monitoring. This paper presents QMON, a practical methodology that leverages mid-circuit measurements and reset operations to monitor the internal states of quantum circuits while preserving their original runtime behavior. QMON enables the instrumentation of monitoring operators at developer-specified locations within the circuit, allowing comparisons between expected and observed quantum-state probabilities at those locations. We evaluated QMON by analyzing its impact on circuit behavior, monitoring coverage, and effectiveness in bug localization. Experimental results involving 154 quantum circuits show that all circuits preserve their intended functionality after instrumentation and that QMON successfully detects and localizes various programming errors. Although monitoring coverage is limited by the need to preserve delicate quantum properties, such as entanglement, QMON effectively detects errors while introducing no or negligible disturbance to the original quantum states. QMON facilitates the development of more robust and reliable quantum software as the field continues to mature.