Non-contact mapping of magnetic fields produced by the human heart muscle requires the application of arrays of miniature and highly sensitive magnetic field sensors. In this article, we describe a MEMS technology of laminated magnetoelectric heterostructures comprising a thin piezoelectric lithium niobate single crystal and a film of magnetostrictive metglas. In the former, a ferroelectric bidomain structure is created using a technique developed by the authors. A cantilever is formed by microblasting inside the lithium niobate crystal. Metglas layers are deposited by magnetron sputtering. The quality of the metglas layers was assessed by XPS depth profiling and TEM. Detailed measurements of the magnetoelectric effect in the quasistatic and dynamic modes were performed. The magnetoelectric coefficient |α32| reaches a value of 492 V/(cm·Oe) at bending resonance. The quality factor of the structure was Q = 520. The average phase amounted to 93.4° ± 2.7° for the magnetic field amplitude ranging from 12 to 100 pT. An AC magnetic field detection limit of 12 pT at a resonance frequency of 3065 Hz was achieved which exceeds by a factor of 5 the best value for magnetoelectric MEMS lead-free composites reported in the literature. The noise level of the magnetoelectric signal was 0.47 µV/Hz1/2. Ways to improve the sensitivity of the developed sensors to the magnetic field for biomedical applications are indicated.