The second generation of the Zaporozhets was a series of subcompact cars, production starting o the 966 in November 1966, although the prototype was ready as early as 1961. It had a completely restyled bodywork, no longer resembling the Fiat 600, though arguably similar to the Chevrolet Corvair or the NSU Prinz It was an effort to cure some of the 965's issues, such as torsion bars that lost tension, suicide doors, and engine overheating and noise. The engine was the 30 hp (22 kW; 30 PS) 887 cc (54.1 cu in) MeMZ 966A. A radio was standard equipment.

While featuring a larger two-door saloon body, it still featured an air-cooled V4 engine and featured more prominent air intakes – the so-called "ears", although a decorative chrome grill was also present. The car's rear suspension was also replaced. The 966 started out as the simpler ZAZ-966V (ЗАЗ-966В in Ukrainian) with the 30 hp (22 kW; 30 PS) engine from the 965A, which was also featured on all later models. Much like the 965A, the 966V was also produced in several special variants for the disabled (VR, VB, VB2 - until January 1973). It was produced in tandem with the 965 from November 1966 to May 1969.

The 966 was discontinued in 1972, with the introduction of the ZAZ 968.