Mladenovic looked like she was going to send the match to the decider as she took an early lead in the tiebreak, but was denied by the No. 2 seed.
Last month, the world No. 63-ranked Frenchwoman hired Sascha Bajin, a sought-after coach. Bajin was coming off a well-publicized split from Naomi Osaka just 16 days after she won her second consecutive major, at the Australian Open, and took over the No. 1 ranking.
Mladenovic, who entered Madrid as a qualifier, had been without a coach for over three years.
"I'm a perfectionist and the discussion we had in the past, why I had only my mom and the people I had around me is because I really only look for the best," Mladenovic told reporters at the Mutua Madrid Open.
Kvitova, who became the first WTA player to win multiple titles this season after claiming Stuttgart—she also won Sydney in January—is aiming for her fourth trophy in Madrid, having won in 2011, 2015, and 2018.
Up next for the 29-year-old Czech is either Caroline Garcia or Sorana Cirstea.