The public prosecutor ordered Saleh al-Mulla held for 10 more days after detaining him late Tuesday about comments made on Twitter, lawyer Abdullah al-Ahmad told AFP.
Ahmad said his client was accused of writing comments on Twitter deemed "offensive" to Kuwait's emir and "humiliating" for Egyptian President Abdel Fattah al-Sisi, who concluded a two-day visit to Kuwait on Tuesday.
Mulla was also accused of threatening Kuwaiti-Egyptian relations by criticising Sisi, the lawyer said.
Ahmad said he will file a petition on Thursday to the court requesting that his client be freed.
In his tweets, Mulla repeatedly urged Emir Sheikh Sabah al-Ahmad Al-Sabah not to give more financial aid to Sisi.
In one tweet, he said any money given to Sisi should be taken back by Kuwaitis.
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Kuwait along with other Gulf states backed Sisi following the military overthrow of Islamist president Mohamed Morsi in July 2013. It has offered Cairo aid worth some $4 billion.
Mulla was an MP for several years before he boycotted elections in December 2012 in protest at the government's amendment of Kuwait's electoral law.
Other opposition activists had launched an online campaign against Sisi's visit, urging authorities not to give more funds to Egypt.
Ahmad said there was no legal justification for Mulla's detention and demanded his immediate release.
Kuwaiti courts have handed down prison sentences to several opposition activists and former lawmakers for remarks deemed insulting to the emir.
The latest ruling was issued on Monday when the supreme court sentenced activist Sager al-Hashash to 20 months in prison on charges of insulting the ruler on Twitter.
Criticising the emir in Kuwait is considered a state security offence, with those found guilty facing up to five years behind bars.