This study reports the creation of a highly sensitive, low-frequency magnetic field sensor based on a composite multiferroic consisting of a bidomain lithium niobate / metglas laminate shaped in form of a tuning fork. An efficient suppression of acoustic and thermal noises in the measurements of AC magnetic fields has been achieved. As a piezoelectric component we used a y+128°-cut lithium niobate single crystal. A metglas foil (serving as a magnetostrictive component) was asymmetrically bonded to each tine of the tuning fork. The sensor demonstrated a 6.7 times increase of the sensitivity to magnetic fields as compared to a single-plate magnetoelectric (ME) sensor: the magnetic field detection limit was enhanced from 20 pT to 3 pT at a frequency of ca. 318 Hz, without any additional shielding from external noises. The advantages of the ME sensors based on bidomain lithium niobate over those based on PZT or PMN-PT are a much higher thermal and chemical stability, non-hysteretic piezoelectric effect, large resistance to creep and ageing effects, lead-free nature and simple and cheap fabrication process. Ultimately, the tuning-fork ME sensors based on bidomain lithium niobate single crystals might be used in low frequency, ultra-sensitive, cheap and high-temperature magnetic field sensors for biomedical or space applications.