In 1979, the 968 series was replaced by the modernized 968M. Prototyped in 1977, it had the "ears" removed and replaced much of the chrome exterior with black plastic. Its interior design was also upgraded, featuring a closed-space glovebox and a slightly more modern dashboard. It was offered with either the MeMZ 968E (40 hp (30 kW; 41 PS), carbureted, low-compression for 76-octane fuel); 968GE (40 hp (30 kW; 41 PS), dual carburettor); or the MeMZ 968BE (50 hp (37 kW; 51 PS), 8.4:1 compression, for 93-octane). Instead of the side-mounted "ears", the hood lid and rear quarter panels were louvered.

The 968M is the most contemporary Zaporozhets model and also spent the most time in production, spanning a career from 1979 to 1 June 1994. Some of its special variants include the ZAZ-968MB2, for drivers who have only one foot, the ZAZ-968MB for drivers who have no feet. Planned 968s with 1,300 cc (80 cu in) or 1,400 cc (90 cu in) engines were never realized.