Heinrich Friedrich Wilhelm Martin Sahm (12 September 1877 – 3 October 1939), no party affiliation, was a German lawyer, mayor and statesman from the Free City of Danzig.
Sahm was born in Anklam, present-day Mecklenburg-Vorpommern and educated as a lawyer, in 1906 he became a member of the Magdeburg city council and served from 1912 to 1919 as a deputy mayor of Bochum. In the meantime he also worked in the government of occupied Warsaw during World War I.
In 1919 he was elected mayor of Danzig (Gdańsk), a city that had formerly belonged to the German Empire. In the same year Danzig and the surrounding territory was to be severed from Germany and turned into a city-state according to the Versailles treaty. After the establishment of the Free City of Danzig in 1920, Sahm became first President of the Senate, the de facto head of state beneath the High Commissioner of the League of Nations. Sahm protested against the take-over of the sea resort town (Ostseebad) Westerplatte by the League of Nations and Poland's establishment of a military transport depot. He held the office until 1931, re-elected two times.