Best Buy CEO Corie Barry says she is cooperating with an investigation into allegations she had an inappropriate romantic relationship with a fellow executive, who has since left the company. Photo: Sarah Silbiger/Bloomberg News

The board of Best Buy Co. BBY 1.11% is investigating allegations that Chief Executive Corie Barry had an inappropriate romantic relationship with a fellow executive, who has since left the electronics retailer.

The allegations were sent to the board in an anonymous letter dated Dec. 7. The letter claims Ms. Barry had a romantic relationship for years with former Best Buy Senior Vice President Karl Sanft before she took over as CEO last June. The Wall Street Journal reviewed a copy of the letter earlier this week.

“Best Buy takes allegations of misconduct very seriously,” a spokesman told The Wall Street Journal. The Minneapolis company said its board has hired the law firm Sidley Austin LLP to conduct an independent review that is ongoing.

“We encourage the letter’s author to come forward and be part of that confidential process,” the Best Buy spokesman said. “We will not comment further until the review is concluded.”

Ms. Barry didn’t address the allegations and said she is cooperating with the probe. “The Board has my full cooperation and support as it undertakes this review, and I look forward to its resolution in the near term,” she said in a statement.

Mr. Sanft, former senior vice president of retail operations, had no immediate comment for this article. He is now the chief operating officer of 24 Hour Fitness Worldwide Inc.

Both Ms. Barry and Mr. Sanft joined Best Buy about 20 years ago and rose through the leadership ranks. By 2008, he was a senior vice president in the sales operation, according to LinkedIn. Ms. Barry became a senior vice president in the finance operation in 2013. She rose to interim president of the company’s Geek Squad division in 2015 and became chief financial officer in 2016.

Ms. Barry, 44 years old, is one of the youngest CEOs of an S&P 500 company and one of the few women. She succeeded Hubert Joly, who led a turnaround at the retailer and still serves as its executive chairman.

Mr. Joly’s predecessor as CEO resigned abruptly in April 2012 after the board opened an investigation into his personal conduct. The company was exploring whether he misused company assets in the course of an alleged relationship with a female subordinate, the Journal reported at the time.

The company’s founder, Richard Schulze, stepped down as chairman in May 2012 after the board-supervised investigation found that Mr. Schulze didn’t alert other directors that the CEO was allegedly having an inappropriate relationship with an employee.

The 2012 probe concluded the former CEO, Brian Dunn, engaged in an “extremely close personal relationship” with a 29-year-old subordinate that “negatively impacted the work environment,” though it found no evidence that he misused company assets.

Senior leaders have been under scrutiny for improper relationships with other employees, especially in the wake of the broader “Me Too” movement. The letter to Best Buy’s board references ousted McDonald’s Corp. CEO Steve Easterbrook, who was terminated last year over a relationship with an employee.

Write to Sarah Nassauer at sarah.nassauer@wsj.com and Dana Mattioli at dana.mattioli@wsj.com

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