Ahmet Necdet Sezer, the president, rejected the ruling Justice and Development Party's (AKP) choices for governor and two more deputies on 23 March.
The prime minister's office announced the veto two days later.
The governor candidate was Adnan Buyukdeniz, who leads the interest-free finance group Albaraka Turk, which operates according to Islamic law.
Erdem Basci was appointed interim governor and Tayyip Erdogan, the prime minister, has said a new candidate to lead the bank will be decided by the cabinet. No date has been announced.
The veto is a setback for Erdogan and comes amid criticism of the government's handling of the appointment process, which hurt bonds, the lira currency and the stock market last week.
Analysts expect financial markets to fall on Monday, the first day of trading since the veto was announced.
Financial markets have been nervous over failure to quickly pick a successor to respected Sureyya Serdengecti, who retired on 14 March after overseeing Turkey's recovery from a deep financial crisis in 2001 with the help of the IMF.
Ali Babacan, the economy minister, told state-run news agency Anatolian that "Turkey has a free exchange rate regime and this will never change...The central bank's fundamental priority is price stability and this will never change".
Babacan said the government backed the central bank's independence.
"Turkey has a free exchange rate regime and this will never change...The central bank's fundamental priority is price stability and this will never change"
Turkish minister of economy
His comments come after market concerns that the bank will come under pressure to weaken the lira and trim high interest rates as political parties begin preparing for presidential and parliamentary elections next year.
Turkish newspapers criticised the government for what should have been a straightforward transition given it was known in advance and the cabinet knew Sezer would be highly likely to veto a candidate with an Islamic-orientated background.
The AKP has been accused of using powers of appointment to put supporters with Islamist principles in top positions at public institutions.