Managing quantum variables in quantum programs presents specific challenges due to the possible occurrence of entanglement, the quantum mechanical phenomenon for which two variables can reach a state where they cannot be separated into two distinct individual states. Such a phenomenon may lead to critical issues due to unintended measurements, which may alter the outcome of computations involving entangled variables. To address this problem, we propose a static analysis based on the abstract interpretation framework to soundly and automatically detect entanglement occurring in quantum programs. By constructing an abstract domain for the entanglement property, our analysis identifies cases where side effects from quantum operations may produce unwanted entanglement, thus reducing the possibility of unintended computational side effects.