Mustafa Geyikçi was born in Turunçova Çavdır in 1958. After completing his primary education at Çavdır Primary School and his secondary education at Finike Secondary School, he completed his high school education at Istanbul Kabataş Boys' High School. He graduated with a bachelor's degree from the Department of Finance and Accounting at the Istanbul Academy of Economics and Commercial Sciences in 1978.

While continuing his commercial activities in citrus, he served as a Member of the Turunçova Municipal Council between 1984-1994, a Member of the Provincial General Assembly between 2004-2014, and a Member of the Finike Municipal Council between 2014-2019. He was then elected as the Mayor of Finike as the candidate of the Nation Alliance in the 2019 Local Elections. In 2024, he was re-elected as the Mayor of Finike as the candidate of the Republican People's Party. He is married, has two children (one daughter and one son), and two grandchildren.