More than 90 people died in the violence and hundreds were injured.
Mr Suthep and former prime minister Abhisit Vejjajiva are co-defendants in the case. Mr Abhisit has been indicted but Mr Suthep's indictment has already been postponed three times.
He was due to report to the Office of the Attorney General today, Thursday.
Mr Suthep assigned a lawyer to submit a request for another postponement, until March 13, explaining that he was still busy leading the political protests demanding the caretaker prime minister's resignation and reforms before an election.
Nanthasak Poonsuk, chief of the Special Cases Litigation Office, said he would ask Department of Special Investigation investigators to issue a summons for Mr Suthep to report to the OAG.