The reshuffle appears to keep in place President Recep Tayyip Erdogan's commitment to market economics following years of financial turmoil.
Erkan had won major plaudits from Western investors for spearheading a rapid series of interest rate hikes that helped stabilize the Turkish lira.
But the 44-year-old came under withering attack on social media and in some opposition publications for allegedly allowing her father to make unauthorized personnel decisions at the bank.
"A major reputation assassination campaign has recently been organized against me," Erkan said in a social media statement announcing her resignation.
Karahan started his career as an economist at the Federal Reserve Bank of New York in 2012.
His official biography states that he also lectured at Columbia University and New York University.
He joined Amazon in 2022 and was appointed as Erkan's deputy at the central bank last July.
Erdogan had selected Erkan to join a team led by Finance Minister Mehmet Simsek and other market-friendly technocrats just weeks after winning the presidential elections last May.
Their reforms have helped Türkiye start winning back foreign investments. Erkan resigned just a week after completing a historic series of interest rate hikes that have pushed the baseline rate from 8.5 percent to 45 percent.
The bank said last week that it intends to keep rates high for the immediate future to make sure inflation is brought under control.
Simsek called Erkan's decision "completely personal" and in no way reflective of Türkiye's future economic policies.
"Our economic program, carried out under the leadership of our President Recep Tayyip Erdogan, continues decisively and without interruption," he said in a statement.
"We will continue to take firm steps towards our price stability target," Simsek said.
Some analysts said Erkan's resignation could actually help Simsek and his team pursue their program by removing a distracting scandal.
"I do not think that the resignation of the central bank governor will have a negative impact," Ankara's TOBB University of Economics and Technology professor Fatih Ozatay said.
"Moreover, this is a development that will take the pressure off the central bank."
Veteran emerging market analyst Timothy Ash called Karahan a "respected ex-NY Fed economist."
"Crisis over," Ash said in a social media statement. "The departure of Erkan has nothing to do with policy — just personal HR related."
Karahan becomes Erdogan's sixth central bank governor since 2019.