Bob Eddy, who has been the company's finance chief since 2011, will take over as CEO on an interim basis, the wholesale retailer said.
Delaney, a former Bain Capital partner, took over as BJ's CEO in early 2020, guiding it through the COVID-19 crisis and supply challenges driven by consumers stockpiling everything from cleaning supplies and toilet paper to fresh meat.
BJ's stock had more than doubled during Delaney's time at the helm, with the company consistently beating quarterly sales estimates through the last year.
The company's shares fell about 1.3% to $44.21 in morning trade.
"We expect to announce permanent changes to our leadership within a reasonably short timeframe," Executive Chairman Christopher Baldwin said.
(Reporting by Uday Sampath in Bengaluru; Editing by Devika Syamnath)
