Nasr has apologised for the remark, describing it as a "error of judgement" to praise Fadlallah without any context, although she said she had been referring to his "pioneering" stance on women's rights.
Fadlallah was branded a terrorist by some Western governments, but issued religious edicts banning so-called honour killings of women and enshrining the right of women to defend themselves from domestic abuse.
In a blog posting after the incident, Nasr wrote that Fadlallah was "revered across borders yet designated a terrorist. Not the kind of life to be commenting about in a brief tweet. It's something I deeply regret".
CNN management decided that Nasr, who had worked at the company for 20 years in mainly off-screen roles, should leave her job. "We have decided that she will be leaving the company," said a company memo circulated on Wednesday.
Fadlallah was a divisive figure who was often described as the "spiritual guide" of Hezbollah, the Shia Lebanese political party. However, he never held a role within the organisation.
He did support some of its actions, endorsing suicide attacks against Israel and was placed on a terrorist blacklist by the US.
But his stance on women's rights and criticism of suicide attacks that targeted civilians led to him being condemned by conservative Islamic scholars who did not agree with his more moderate views.