Suthep, who is trying to topple the caretaker government, is facing a charge of insurrection.
CAPO member Tarith Pengdit, who is also chief of the Department of Special Investigation, said he had signed the summons against Surachai based on the suspicion that he was attempting to have an unelected prime minister put place under an interpretation of Article 7 of the Constitution.
Surachai has been ordered to report tomorrow at 2pm.