Chris Sherrell was named acting chief executive officer following Saturday's resignation of company Chairman and CEO Michael Gilliland, Sunflower Farmers Market said on its Web site. Gilliland also quit his post on the Phoenix company's board of directors.
Company board member Bennett Bertoli was elected chairman by the board.
Sherrell will continue to hold the positions of president and chief operating officer.
"Sunflower appreciates the respect that Mr. Gilliland has shown for the company by his action, so that his personal affairs will not affect the company," Sherrell said.
The Arizona Republic reported police said Gilliland, 52, was arrested at a hotel on suspicion of felony child prostitution. Sgt. Steve Martos said it is alleged the businessman knew he was going there with the intention of paying a minor, whom he had met online, for sex.
He said Gilliland was one of eight people arrested as part of an ongoing investigation.
The company statement said Gilliland has informed the company he believes he is not guilty of the charges and expects to be exonerated.
Sunflower Farmers Markets, founded by Gilliland in 2002, has 32 stores in Arizona, Colorado, New Mexico, Nevada, Texas and Utah.