Managing quantum variables in quantum programs presents specific challenges due to the possibility of emph{entanglement}, a quantum mechanical phenomenon for which two variables can be in a state where their individual states cannot be separated so that they form, indeed, a single system rather than the composition of two. This can 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 mitigating unintended computational side effects.