Eilidh Mactaggart, who was appointed chief executive in 2020 on a salary of £235,000 a year, sparked a secrecy row after quitting her role with no public explanation.
In a statement, Ms Mactaggart said she stood down for “personal reasons”.
She said: “My decision to resign from my position as chief executive of the Scottish National Investment Bank was a difficult decision to make, but ultimately it was made for personal reasons.
"I am extremely proud of everything I achieved while I was the bank’s chief executive, including launching a bank in the midst of a global pandemic while working remotely, setting its investment strategy, and establishing its investment portfolio.
"I am, of course, most proud of the incredible team of talented individuals that the bank now has in place, all bound by a common purpose to deliver investment to businesses and projects connected to Scotland to support the bank’s missions.
“It was a privilege to be given the challenge of launching the Scottish National Investment Bank and being its inaugural chief executive and I wish the team I have built all the best for the future.
"I am considering a number of opportunities and looking forward to spending some more time with my young family in the meantime.”
SNIB, a public body, was launched in November 2020 and makes investments in Scottish firms and projects.
Ministers have pledged funding of £2 billion over its first ten years.
Speaking in Holyrood on Thursday, Ms Sturgeon said: “Everyone across the chamber will understand that I’m not going to go into the confidential details of anybody’s employment situation here in the chamber.”
She added: “This issue is not a matter for Scottish Government ministers, it’s a matter for the board of the Scottish National Investment Bank. Ministers had no input into that, although we were told earlier in February that the chief executive would be leaving the bank imminently.”