Surapak Phuchaisaeng was arrested in Bangkok on Friday, said a senior police officer at the Technology Crime Suppression Division.
Under Thailand's controversial lese majeste legislation, anybody convicted of insulting the king, queen, heir or regent faces up to 15 years in prison on each count.
Surapak, who also faces related charges under the Computer Crime Act, is one of the first people arrested for insulting the monarchy since a new government took power last month.
Prime Minister Yingluck Shinawatra said after her July 3 election win that the rules should not be misused, following several high-profile cases against supporters of her brother Thaksin, Thailand's fugitive former leader.
But in a sign she did not want a direct confrontation with the country's powerful elites, her government has since vowed to set up a "war room" to crack down on alleged online royal insults.
Earlier this month more than 100 international academics called on Thailand to review the tough laws, saying political abuse of the legislation is undermining human rights.
The laws have come under heavy criticism from rights groups, which have expressed concern that they have been used to suppress freedom of expression under the last government, considered close to the establishment.
In March, a webmaster was jailed for 13 years after the Internet site he ran, linked to the opposition movement, allegedly published comments insulting the monarchy.
Another website editor currently on trial faces decades in prison if convicted -- for failing to remove reader comments quickly enough.
Discussion of the royal family's role is a long-standing taboo in politically divided Thailand.
King Bhumibol Adulyadej, 83, the world's longest-reigning monarch and revered as a demi-god by many Thais, has been in hospital since September 2009.