ISTANBUL—Turkey’s national election board canceled results of the Istanbul mayoral race that President Recep Tayyip Erdogan’s ruling party lost five weeks ago and ordered a rerun, sparking outrage in opposition ranks and fueling investor concerns over heightened economic volatility.

Ruling on complaints filed by Mr. Erdogan’s Justice and Development Party, or AKP, the election board said a new vote was necessary because fraud and irregularities had material influence on the March 31 results in Istanbul. The ruling is final...