A lower court imposed the sentence on Abdullah Fairouz Abdullah Abdel-Kareem, 30, on January 9 for posting comments on the microblogging website deemed offensive to the emir.
The court also ordered Abdel-Kareem to be deported after serving the jail term although he has the right to Kuwaiti citizenship.
The court acknowledged that Abdel-Kareem had won a final court ruling over his right but he has so far not obtained the citizenship card and thus the court treated him as a foreigner.
Under Kuwaiti law, foreign residents are deported by courts if they receive jail sentences for any serious crime.
Abdel-Kareem's mother is Egyptian and his father Kuwaiti. It is not clear what passport he carried when he won the right to Kuwaiti citizenship.
"The judgment against Kareem is shocking," said Nadim Houry, deputy Middle East and North Africa director at Human Rights Watch (HRW).
"We hope that the exile sentence is not a new strategy by the prosecution to chill political commentary in Kuwait," he said.
Abdel-Kareem is not a member of the Kuwaiti opposition but a prominent rights activist.
The New York-based HRW said that Kuwaiti authorities should drop the charges and not contest Abdel-Kareem's already lodged appeal.
"Since a political crisis in June 2012, Kuwaiti authorities have ramped up efforts to limit free expression, with courts sentencing at least 18 politicians, online activists, and journalists to prison terms for 'offending' the emir," HRW said.
"Kuwait has made clear through the recent string of cases that it is willing to trample on people's rights to protect the emir from criticism," it said.
HH/HH