Naoot, a former parliament candidate, is the second public figure to receive a jail term in less than a month for charges related to blasphemy, the paper said.
The jail sentence is effective immediately, although Naoot will be able to lodge an appeal from behind bars.
In October, she described in a post on her Facebook account Eid Al-Adha's tradition of slaughtering sheep as the "greatest massacre committed by human beings".
Naoot also wrote in an article in Egyptian daily El-Masry El-Youm criticizing the traditional slaughter of sheep during Eid, the Islamic festival of sacrifice and one of the main Muslim religious holidays worldwide.
During questioning, Naoot admitted writing the Facebook post but denied that her aim was to insult Islam, Al-Ahram said.
Naoot argued that humans justified their lust for killing and enjoying the smell of cooking game by attempting to bestow a divine meaning to their actions.
Egyptian authorities put TV host Islam Behery in prison in December after a court reduced to one year an earlier five-year sentence against him for "contempt of religion" over comments he made questioning the credibility of some sayings of the Prophet Mohammed on his now-suspended TV programme.
El-Beheiry is appealing against his prison sentence. His trial sparked public controversy and he got the support of many journalists, writers, scholars and human rights activists.
El-Beheiry and Naoot's convictions come amid public debate over freedom of speech in Egypt.
The nascent Egyptian Secularist Party launched a campaign in November calling for the repeal of an Egyptian law punishing contempt of religion with up to five years in prison, Daily News Egypt reported.