The aim is to create an exhaustive list of current sensor manufacturers. Hence please do contact us or comment if we have missed a company out.
For background on how these devices work and where they sit in the battery system, see our overview of the current sensor.
Isabellenhuette
Isabellenhütte Heusler is one of the oldest industrial companies which is first mentioned as early as 1482. The company named in 1728 as “Isabelle Kupferhütte” and in 1827 the Heusler family acquired the company. The company specialized in very high precision resistive elements and measuring technology.
Company URL: https://www.isabellenhuette.de/en/precision-measurement/applications/electromobility
LEM
LEM SA (Liaisons Electroniques-Mécaniques) established in 1972 in Switzerland. The company specialized in high-quality transducers for measuring electrical parameters. LEM has a wide market for different areas such as variable speed drives for motors, power supplies for industrial applications, AC/DC converters, new innovative energy applications, as well as automotive applications.
Company URL: https://www.lem.com/en/automotive-battery-management
QULECTRA
QULECTRA is a joint venture of Wieland-Werke AG based in Ulm and Munich Electrification GmbH based in Munich. The two companies share a multi-year partnership in the provision of battery management systems with shunt-based precision resistors. With QULECTRA, we are taking the next step in the development of best-in-class current sensors that point the way to a sustainable future.
Company URL: https://www.qulectra.com/
TE Connectivity
TE Connectivity is a global company specialized in different areas like sensor and connectivity solutions for data, signals and power systems. The company manufactures also current sensors for EV applications.
https://www.te.com/usa-en/industries/sensor-solutions/applications/sensors-e-mobility-ict/ev-battery.html

For a deeper look at shunt vs. magnetic (Hall and fluxgate) sensing elements and the boundary conditions that drive sensor selection, see EV Current Sensors: The Basics.
See also: BMS Sensors