The former banker had been in charge of the day-to-day running of the club, having been appointed by previous owner Carson Yeung in January 2014.
He steered the Championship club through difficult financial circumstances, before a takeover by Trillion Trophy Asia (TTA) in 2016.
A Birmingham City statement said Pavlakis had "left to pursue other opportunities".
Pavlakis, who has also relinquished his position on the board of Birmingham City Ladies, was brought into the club by Birmingham International Holdings.
He oversaw the appointment of Gary Rowett as manager in 2014, before replacing him with Gianfranco Zola in December 2016.
The Italian lasted just four months in charge before resigning in April, when Harry Redknapp took charge of the final three games of the campaign, before agreeing a deal to continue in the role next season.
Richard Wilford, BBC WM
For many Birmingham City supporters this season, Panos Pavlakis became the head of blame - the Greek ex-banker is viewed as the man who ended the successful Rowett era at St Andrew's in favour of the shambolic Zola experiment.
Whatever the intentions of Pavlakis and Trillion Trophy Asia were, the sudden shift in emphasis on the playing side of the club saw them flirt with disaster.
However, history should reflect more kindly on the man who guided a troubled club out of the hands of disgraced imprisoned owner Yeung and into the potentially more stable environment of TTA.
Pavlakis was the public face of the club through two years of voluntary receivership, helping accountancy firm Ernst and Young to sift through a fiercely tangled financial mess in order to make Birmingham City saleable.
Last week, Pavlakis told me his trip to Hong Kong this month was likely to be the end of the road for him. TTA had not seen fit to appoint a chief executive or managing director at St Andrew's, and his role was diminishing.
He would not have relished a job that largely consisted of bean-counting.
His legacy should be that of a solvent Birmingham City, rather than just as the man who appointed Zola.
Director Panos Pavlakis has resigned from the board at Birmingham City.