TV footage showed police breaking up the fight outside the mission as voting for the November 1 election began early in the Japanese capital.
The injured included two police officers, Tokyo Broadcasting System said, adding that the cause of the fight was not immediately clear.
But Jiji Press, quoting a Turkish voter, said the clash began after Kurds tried to display the flag of a pro-Kurdish party.
Some 3,600 Turkish nationals are resident in Japan, according to the country's foreign ministry.
More From This Section
The election comes at a time of escalating violence in Turkey's mainly Kurdish southeast, despite a 2013 ceasefire in a three-decade insurgency that has claimed tens of thousands of lives.
Turkish President Recep Tayyip Erdogan called the poll after his ruling Justice and Development Party (AKP) lost its governing majority for the first time in June 7 elections, forcing it into coalition talks that ended in failure.
The result damaged Erdogan's hopes of creating a powerful US-style presidency with full executive powers.