Although other surfaces have used the system, the clay event is largely the same as the lineman, or the referee descending from his or her chair to check the ball left when the call is called.
However, judges this season have been removed from all events on the ATP Tour, and many have been removed on the WTA Tour.
However, the French Open, which begins next month, will also continue with the line judges.
It was the latest controversial call incident in which world No. 1 Aryna Sabalenka took photos at Stuttgart earlier this month, while former Grand Slam champion Victoria Azarenka posted another Madrid match on social media.
Elsewhere in the Spanish capital, defending champion Andrey Rublev lost 6-4 0-6 6-4 to Alexander Bublik – a defeat that would put the Russians out of the world's top 15.
In the women's draw, top seed Sabalenka recovered to defeat Elise Mertens 3-6 6-2 6-1 due to losing the opening scene.
But the third seed, Jessica Pegula and the sixth seed, Jasmine Paolini, were both eliminated.
American Pegula was frustrated 6-3 6-2 in Japan's Moyuka Uchijima, while Italian Paolini beat 6-2 6-1 in the hands of Greece's Maria Sakkari.
