BEIJING—Authorities are investigating the sudden death of the top anticorruption official at one of China’s largest oil companies, say people familiar with the investigation, a matter that is roiling Beijing’s political elite.

Zhang Jianwei, who was helping to lead a Communist Party-ordered clean-up of graft and other alleged wrongdoing at China National Offshore Oil Corp., was found dead around lunchtime on Nov. 3 at his office, these people say.

Authorities...