Following the competitive but modest results of the MS650, Matra's engineering team developed the MS660 as a more advanced prototype intended to mount a stronger challenge in the International Championship for Makes. Like its predecessors, the car was run under the Matra-Simca banner reflecting the partnership with Simca. The MS660 ultimately served more as a development platform than a title contender, plagued by retirements and clouded by tragedy before giving way to the MS670 chassis.
The MS660 made its debut at the 1970 24 Hours of Le Mans, where Matra entered three cars in a mixed deployment alongside the older MS650. Jean-Pierre Beltoise and Henri Pescarolo drove the new MS660, while Jack Brabham paired with François Cevert, and Patrick Depailler with Jean-Pierre Jabouille and Tim Schenken, ran MS650s. All three cars retired with engine failure, leaving the team without a classified result. Matra's four championship points that season were scored entirely by the MS650 in earlier races; the MS660 itself failed to contribute to the tally. The team finished fourth in the championship.
The 1971 season began at the 1000 km of Buenos Aires, where Matra entered a single MS660 for Beltoise and Jabouille. The car ran out of fuel and was pushed back towards the pits by Beltoise. Race leader Ignazio Giunti, driving a Ferrari, struck the disabled MS660 at speed. Both cars caught fire and Giunti died from his injuries, making the incident one of the darkest moments of the early 1970s sports car season. Following the accident, Beltoise had his international racing licence suspended for a period.
The team made no further entries until the 24 Hours of Le Mans, where Beltoise partnered Chris Amon. Their MS660 retired with a fuel system failure. Matra scored no championship points during the 1971 season.
For 1972 the MS660 continued in an updated form designated the MS660C. Matra entered Jabouille and David Hobbs at the 24 Hours of Le Mans, the car's final major appearance in competition. It retired with a transmission problem. No points were scored. The MS660 was retired from front-line duty after the 1972 season, replaced by the new Matra-Simca MS670 that would go on to dominate the World Championship for Makes in 1973 and 1974.
The MS660's competitive record was modest, marked by mechanical failures and the tragedy at Buenos Aires. Yet the car served a necessary developmental function within Matra's endurance program, refining the team's technical approach and providing crucial high-speed data that informed the design of the MS670. Drivers such as Beltoise, Pescarolo, Jabouille, and Amon who campaigned the MS660 would form the core of Matra's later championship-winning efforts, demonstrating the continuity of the works program even through its difficult middle years.