Turkish media pictures earlier showed Sumeyye, 30, wearing an Islamic headscarf, sitting in the front seat of the black BMW bridal car.
Erdogan and his wife Emine have four children -- eldest son Burak, Bilal and two daughters Esra and Sumeyye.
The wedding started with the reciting of Koran, the private NTV television reported.
Top officials including Prime Minister Ahmet Davutoglu, army chief Hulusi Akar and former president Abdullah Gul attended the ceremony, to which some 6,000 guests were reportedly invited.
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Davutoglu's appearance at the wedding could dismiss claims of a split with the president.
In a surprise move, Davutoglu last week announced he would step down as premier and leader of the ruling Justice and Development Party (AKP) at a congress later this month.
A heavyweight former foreign minister, he is believed to have been forced out of office due to repeated disagreements with Erdogan and that the key quality in the next head of government would be loyalty.
The high-profile wedding forced the closing of several roads to traffic In Istanbul and additional barriers were put up around the wedding hall in Kucukcekmece on the European side of the city, media reports said.
She served the AKP government on foreign policy issues when Erdogan was prime minister but after her father was elected president in 2014, she quit that post.
She now works as the deputy head of the non-govermental group Women and Democracy Association (KADEM).
The groom Bayraktar graduated from Istanbul Technical University's department of electronic engineering in 2002.