"A major reputation assassination campaign has recently been organized against me," Erkan said in her statement, referring to recent defamation campaign launched against her on social media.
She added that she was stepping down "in order to prevent my family and my innocent child, who is not even one-and-a-half years old, from being further affected by this process."
She thanked President Recep Tayyip Erdoğan and expressed her gratitude for his support during her term.
On Wednesday, Erdoğan decried efforts to spread "rumors" meant to undermine economic progress, in an apparent endorsement of Erkan, who had criticized a recent press report about her family.
"When the central bank's reserves reached a record-breaking $145.5 billion, they took immediate action. They launched campaigns to disrupt the climate of confidence and stability in our economy with unreasonable rumors, which could undermine the progress we have made," Erdoğan said.
He did not specify the rumors nor reference Erkan directly, though earlier in the speech he cited "opposition" efforts to criticize the government and economy.