Al-Jarida newspaper said the verdict against Orance al-Rasheedi, who was also convicted of spreading false news about Kuwait to undermine the oil-rich country's image, is final and cannot be challenged.
Rasheedi was accused of using the social networking sites Twitter and YouTube to publicly insult the emir, Sheikh Sabah al-Ahmad Al-Sabah, who is protected against criticism by Kuwait's constitution.
The lower court meted out the sentence against Rasheedi in October 2011 and the court of appeals upheld it in May last year.
Kuwait has in the past few months intensified its clampdown on Internet activists who allegedly violate the country's laws, especially since the opposition began staging demonstrations to protest amendments to the electoral law.
The courts have already jailed several activists and many others are awaiting trial.