Intrinsic magnetic noise limits the functionality of most magnetic field sensors. This study investigates the impact of intrinsic magnetic noise on the performance of magnetoelectric magnetic field sensors, at the example of two sensor concepts based on the ΔE effect and the converse magneto electric effect, respectively. Our analysis shows that they exhibit comparable behavior in terms of noise and operational limitations. In both cases, the magnetic properties of the magnetostrictive layer determine the theoretical minimum of the equivalent magnetic noise density. The range of operational parameters with which this minimum can be achieved is constrained by the magnetic noise source linked to the nonlinearity of the magnetostrictive properties. This previously unidentified noise source significantly degrades sensor performance and imposes a strict limit on the acceptable noise level of the nonmagnetic noise sources in the sensor system. Although this noise source is particularly evident in highly magnetostrictive materials, it can be relevant to a wide range of devices incorporating magnetic materials.