Edwards, whom many considered a potential successor to CEO Mark Parker, resigned effective immediately on Thursday, according to an internal memo from Parker, obtained by the Journal. Edwards will retire from the company in August.
The memo said the company had received reports of "behavior occurring within our organization that do not reflect our core values of inclusivity, respect and empowerment."
Parker did not disclose the nature of the complaints or whether they involved Edwards directly. A Nike spokesman told the Journal there were no allegations against Edwards and declined to provide details.
"This has been a very difficult time," Parker wrote in the memo.
Parker said Nike would be reviewing the company's protocol for dealing with internal complaints, the Journal reported. Furthermore, to deal with Edwards' unplanned absence, Parker said he will remain chairman and CEO of Nike beyond 2020.
Nike did not immediately return CNBC's request for comment.