We study the entanglement of a two-qubit system in a superconducting quantum dot (SQD) lattice in the presence of magnetic flux and gate voltage. The ground state is always in a maximally entangled Bell state for homogeneous gate voltage. In the presence of inhomogeneous gate voltage, the half-integer magnetic flux quantum, completely washes out the entanglement of the system at zero temperature. The entanglement is much higher for the Mott insulating phase. At finite temperature, collapse of entanglement occurs for wider region of magnetic flux.