The air force chief, a classmate of Gen Prayuth, holds three positions on the PTT board: independent director, chairman of the nominating committee and member of the corporate governance committee.
ACM Prajin cited "business engagements" as the reason for his resignation, effective on Saturday, PTT president and CEO Pailin Chuchottaworn told the Stock Exchange of Thailand after the market closed on Friday.
Thai media speculated that ACM Prajin would be appointed transport minister while Narongchai Akrasanee would take the energy portfolio.
Visanu Krue-ngam, an adviser to the National Council for Peace and Order (NCPO), said on Friday that it would take a while before the cabinet was formed. Nothing could be done until the prime minister is royally endorsed, he explained.
Gen Prayuth was appointed unanimously as prime minister by the National Legislative Assembly (NLA) on Thursday. He is the first coup leader to also serve as premier since Field Marshal Sarit Thanarat in 1957.
Mr Visanu also said it would take some time to approach competent people to join the cabinet and verify their qualifications.
He said he himself had not been "officially" asked to join the cabinet.
The PTT board on Friday also approved a reshuffle in which Supattanapong Punmeechaow, senior executive vice-president for corporate strategy, will become CEO and president of PTT Global Chemical Plc, a subsidiary of the majority state-owned energy conglomerate.
Atikom Terbsiri, senior executive vice-president for petrochemicals and refining, will become CEO and president of Thaioil Plc, a PTT refining affiliate.