The Beastie Boys rapper, who fought a three-year battle with cancer, was credited with leading a "musical revolution" by the pop superstar.
Madonna, who was supported by Yauch on tour in 1985, said that the rapper was "integral to the musical revolution that was happening at the time".
The 53-year-old also emphasised her sadness, asking God to bless his family.
MCA's death has prompted similarly heartfelt reactions from the likes of Boy George, Snoop Dogg and will.i.am.
The hip-hop icon won three Grammy Awards with his group.
Coldplay performed a tribute to Yauch during a concert in Los Angeles on Friday (May 4).
Photo gallery: Adam Yauch's life and career in pictures:
Copyright: Rex Features Everett Collection