His replacement is expected to be named in the first quarter of 2019.
While the bank said it was "pleased" with Kiknavelidze's achievements as CEO, its shares have fallen 46 percent from a record high hit in early January, erasing almost two years of gains.
In contrast, shares in Bank of Georgia's rival and the country's top retail lender, TBC Bank Group Plc, have fallen 16 percent since the start of the year.
The board of directors, after a period of reflection, had agreed with Kiknavelidze that the time was now right for a new CEO to take the business to its next phase, Bank of Georgia said.
Kiknavelidze, who became CEO in 2016 after more than a decade on the board, will stay on as a senior adviser, the Tbilisi-based company said in a statement.
The bank, which was formed when BGEO Group demerged into two entities in May, also reiterated its annual financial targets on Monday.
Bank of Georgia, which offers retail, corporate and investment banking and wealth management, last month reported a double-digit jump in quarterly earnings, benefiting from higher lending amid strong economic growth in the former Soviet republic.
(Reporting by Muvija M in Bengaluru; Editing by Sai Sachin Ravikumar)