CARACAS, Venezuela—The head of state-run Petróleos de Venezuela SA, Eulogio del Pino, is leaving the company to run for a special assembly charged with redrafting the country’s constitution, according to a person familiar with the matter.

Venezuelan President Nicolás Maduro asked Mr. Del Pino on Thursday to run for the so-called Constituent Assembly, the person said. The oil executive has accepted the request and by law will abandon his post at the state oil company in the coming days.

The...