The M195 was originally designed around a Mugen-Honda engine, which Minardi expected to receive for the 1995 season. A last-minute decision by Mugen to supply the Ligier team instead left Minardi scrambling to adapt the chassis to accept a Ford Motor Company ED engine. Team owner Giancarlo Minardi described the situation bluntly: "We are very proud because we have had to design two different cars in the time normally needed to do just one."
Minardi pursued legal action against Mugen over the engine supply dispute. The court found that the arrangement between the two parties had reached a sufficient stage of mutual agreement that Minardi was legitimately entitled to expect the contract to be concluded. Minardi won the lawsuit, though the court declined to award damages. Minardi appealed that element of the ruling.
In a counter-move during the legal dispute, Flavio Briatore — then owner of Ligier — had Minardi's equipment seized at the French Grand Prix, citing money owed by Minardi to one of his companies relating to an engine arrangement from 1993. The matter was eventually settled out of court: the outstanding debt was waived and Briatore paid Minardi one million US dollars in compensation for the loss of the Mugen-Honda engine deal.
The M195 competed through the 1995 season with Pierluigi Martini and Luca Badoer as the primary driver pairing, the car occupying the back of the midfield throughout. The team faced the twin handicaps of an underpowered engine and a chassis originally conceived for a different power unit, yet still managed to field both cars consistently across the season. A notable livery moment came at the 1995 Australian Grand Prix in Adelaide, where the car carried the message "Grazie Adelaide" — a farewell tribute as the race departed the city it had called home since 1985.
For the 1996 season, the M195 was updated and redesignated the M195B. The most visible change was higher cockpit sides, mandated by new driver safety regulations introduced for that year. Pedro Lamy took one seat; Giancarlo Fisichella, Tarso Marques, and then Giovanni Lavaggi shared the other across the season. The M195B failed to score any championship points.
Both the M195 and M195B carried a black-and-white colour scheme with fluorescent green wings, the distinctive look reflecting sponsorship from Italian furniture companies Doimo and Valleverde.
The M195 represents the period when Minardi operated under some of the most difficult technical and legal pressures in the team's history, yet continued to run reliably and develop young talent. Aldo Costa, who designed the car, would go on to become one of the most decorated engineers in Formula One, later serving as chief designer at Ferrari during their title-winning era with Michael Schumacher and subsequently as engineering director at Mercedes during their dominant hybrid period.