Matra's switch from Group 5 to Group 6 regulations with the MS650 allowed the team to develop a more purpose-built prototype rather than continuing to adapt the MS630 platform. The MS650 retained the 3.0-litre Matra Sports V12 engine that had been introduced in the MS630 for 1968, but its chassis and aerodynamic package were evolved to suit the new regulations and to extract greater competitiveness. The car was backed by Simca's sponsorship, which had also lent its name to the MS630 from 1969 onward.
The MS650 made its competitive debut at the 1969 24 Hours of Le Mans, where it was the centrepiece of a four-car Matra entry that also included an unmodified MS630 and two MS630/650 hybrids. Jean-Pierre Beltoise and Piers Courage drove the full MS650, finishing fourth overall — a strong result for a car making its first appearance at the world's most demanding endurance race.
Later in the 1969 season, the MS650 continued at the Watkins Glen 6 Hours, where Johnny Servoz-Gavin and Pedro Rodriguez shared the car and finished fourth. The final outing of the season came at the 1000 km of Zeltweg, where Matra entered only Servoz-Gavin and Rodriguez, but their race ended in an accident.
Matra scored six points in the 1969 International Championship for Makes, finishing fifth in the manufacturers' standings. All six points came from MS650 entries; the MS630 and MS630/650 cars did not contribute to the tally.
The MS650 carried the team through 1970 as Matra prepared the next-generation MS660 for its Le Mans debut. The season opened at the 24 Hours of Daytona with two cars: Jack Brabham and François Cevert finished tenth, while Jean-Pierre Beltoise and Henri Pescarolo finished eighteenth. At the 12 Hours of Sebring, driver pairings were reshuffled, with Pescarolo and Servoz-Gavin finishing fifth and Cevert and Dan Gurney finishing twelfth.
For the 1000 km of Brands Hatch, Brabham and Beltoise were paired together, finishing twelfth, while Pescarolo and Servoz-Gavin retired with engine failure. At the Monza 1000 km, Brabham and Beltoise took fifth place and Pescarolo and Servoz-Gavin sixth. Matra then skipped the Targa Florio, the 1000 km of Spa-Francorchamps, and the 1000 km of Nürburgring.
The 1970 24 Hours of Le Mans brought a painful result. Matra entered three cars: Beltoise and Pescarolo in the new MS660, and two MS650 entries for Brabham and Cevert, and for the trio of Patrick Depailler, Jean-Pierre Jabouille, and Tim Schenken. All three cars retired with engine failure, leaving the team without a Le Mans finish for the third successive year. Matra did not contest the remaining 1970 rounds, the Watkins Glen 6 Hours and the Austrian 1000 km.
In the 1970 International Championship for Makes, Matra scored four points, finishing fourth in the standings.
The MS650's two-season career produced solid top-five championship finishes without a race victory, but its value lay in accumulating race experience and pointing toward the areas that required development. The recurring engine failures in 1970 were a significant concern that the team addressed in the MS660 and MS670 programmes. When the MS670 finally arrived in 1972, Matra had the technical foundation to win Le Mans outright, a result that the MS650 had helped make possible through two years of hard-learned endurance racing.