Long-serving national coach Low has faced criticism in the wake of the 6-0 defeat to Spain in the Nations League.
Results and performances had been sketchy in the months leading up to November's humiliation in Seville which brought the team's form into sharp focus.
Matthaus, who captained West Germany to 1990 World Cup glory, is now among Germany's leading football pundits and believes Low should not be the only figure to pay the price if Die Mannschaft fail at the European Championship.
Speaking to the Suddeutsche Zeitung, Matthaus said: "If the European Championship does not go as we would like and as we can expect in view of the players, then not only Low would have to pack his suitcase but everyone who decided that he should stay. They too have to bear the consequences."