Three-dimensional (3D) microwave cavities with embedded superconducting quantum bits (qubits), provide a popular and versatile platform for quantum information processing and hybrid quantum systems. A current issue that has arisen is that 3D superconducting cavities do not permit magnetic field control of qubits embedded in these cavities. In contrast, microwave cavities made of normal metals can be transparent to magnetic fields, but experience a much lower quality factor, which negates many of the advantages of the 3D architecture. Here we presented measurements of a device that bridges a gap between these two types of cavities with magnetic field control and an order of magnitude higher quality factor compared to all previously tested copper cavities. An added benefit to that our hybrid cavity possesses is that it also provides an improved thermal link to the sample that superconducting cavities alone cannot provide. A large improvement in quality factor and magnetic field control makes this 3D hybrid cavity an attractive new platform for circuit quantum electrodynamics experiments.