Polke was best known for the Capitalist Realism movement he began in the 1960s, an ironic response to the Soviet Union's official art doctrine of Socialist Realism and the American Pop Art scene.
Klein said that with Polke's death, the German art scene had lost one of its "most colourful personalities."
Polke used the imagery of Pop Art including ordinary foods as a starting point but manipulated them to the point of abstraction, making the familiar foreign.
An avid experimentalist, Polke moved fluidly between styles and media all the while maintaining his signature bemused distance in his work, which also included photography, sketches, installations and collage.
He won many of the coveted prizes of the art world including the Golden Lion of the Venice Biennale in 1986.
Born in Lower Silesia in today's Poland, Polke fled communist East Germany in 1953. He attended the Academy of Fine Arts in the western city of Düsseldorf, where Joseph Beuys was among his teachers.
While still a student, he launched the Capitalist Realism movement with Konrad Fischer-Lueg and Gerhard Richter.
His grid-like works and decorative fabric paintings attracted international attention in the 1960s and he began to explore other materials including even plastic sheeting instead of standard canvases.
Beyond his formal experiments, Polke confronted historical and political issues in his work including Germany's Nazi past, national reunification and the French Revolution.
Culture Minister Bernd Neumann on Friday called Polke "one of the most important and successful representatives of contemporary German art."
"He was a critical, ironic and also self-deprecating observer of post-war history and its artistic commentator," he said.
"With a desire for experimentation, he developed his own language in images. Sigmar Polke, the 'alchemist of colours', leaves behind a unique body of artistic work."