Access to YouTube was blocked on Wednesday after its owner, Google, declined to withdraw a video clip mocking the king.
"Since Google has rejected our repeated requests to withdraw the clip, we can't help blocking the entire site in Thailand," Sitthichai said.
"When they decide to withdraw the clip, we will withdraw the ban."
YouTube, which has dominated the user-generated online video market since it was founded in February last year, carried a 44-second clip ridiculing King Bhumibol Adulyadej, the world's longest reigning monarch revered by all 63 million Thais.
The most offensive part of the clip, viewed more than 16,000 times, was the juxtaposition of a pair of woman's feet, the lowest part of the body to Thai Buddhists, above the monarch's head, the highest part of the body.
Critics have accused the current government of shutting websites criticising the September coup that overthrew the government of Thaksin Shinawatra.
However, Sitthichai said the government is targeting only sites deemed insulting to the monarchy - a criminal offence in Thailand.
The government is also targeting pornographic sites, he said.
One of the sites shut down was launched by an anti-coup group, which calls itself Saturday Voice Against Dictators and has been holding protests demanding that coup leaders transfer power to a democratically elected government.
The group has also accused Prem Tinsulanonda, the king's chief adviser, of playing a role in the coup.
Sitthichai said online remarks considered insulting to the king's advisers would also result in a website being closed.