A video clip was circulated online showing the interview in which Mr Wuthipong made the offensive remark about the monarchy.
Prime Minister's secretary-general Suranand Vejjajiva said Wednesday the premier had ordered him to submit a letter to national police chief Adul Saengsingkaew calling for action against Mr Wuthipong.
Pol Gen Adul called an urgent meeting Wednesday to discuss the case, said Pol Col Vichayakorn Nichabovorn, deputy police spokeswoman.
The police chief was informed by the Technology Crime Suppression Division (TCSD) that Mr Wuthipong's remark in the clip shared on YouTube violates Section 112 on lese majeste in the Criminal Code.
"The TCSD was instructed to contact the Information and Communication Technology Ministry to block access to the clip," Pol Col Vichayakorn said, adding that the ministry was now working on the issue.
According to Pol Col Vichayakorn, Pol Gen Adul also assigned deputy national police chief Ek Angsananon to head the investigation, while assistant police chief Jaktip Chaijinda will be deputy leader of the team.
She added that the Royal Thai Police Office has warned the public not to share the video clip as those doing so will also be subject to punishment under Section 112. Those found guilty are liable for a three- to 15-year jail term.
Democrat Party leader Abhisit Vejjajiva has also instructed the party's legal team to file a complaint against Mr Wuthipong for lese majeste, spokesman Chavanond Intarakomalyasut said.