Thitinant Kaewjantranont has been held for psychological assessment at a health institute in the Thai capital since July 14, according to national police spokesman Piya Utayo.
She is accused of making a disrespectful gesture towards an image of Thailand's King Bhumibol Adulyadej outside the Constitutional Court on July 13 -- the day of a tense ruling that saw the ruling party escape dissolution.
"She was placed under police custody at the institute the next day and is under going mental health checks," Piya told AFP, adding that a Bangkok court had issued the warrant for her arrest on July 16.
The royal family is an extremely sensitive subject in politically turbulent Thailand. The king, who is revered as a demi-god by many Thais, has been hospitalised since September 2009.
Under the legislation, anyone convicted of insulting the Thai king, queen, heir or regent faces up to 15 years in prison on each count.
Observers say lese majeste prosecutions have surged following a coup by royalist generals that removed fugitive former premier Thaksin Shinawatra in 2006. Thaksin's sister Yingluck now leads the government, but the trend is seen as likely to continue.