The court in Istanbul also acquitted Erdogan, who is living in exile in Germany, of disrupting the unity of the state, and dropped charges of spreading terror propaganda.
Erdogan, whose books have been translated into various different languages, was an occasional columnist for pro-Kurdish newspaper Ozgur Gundem which was shut down after the failed 2016 coup against Turkish President Recep Tayyip Erdogan.
Turkish authorities accused the paper -- where Asli worked as a literary adviser -- of being a mouthpiece for the outlawed Kurdistan Workers' Party (PKK), considered a terror group by Ankara and its Western allies.
The court also acquitted two other defendants, including linguist Necmiye Alpay.
The 52-year-old Erdogan -- who is not related to the Turkish president -- was held in pre-trial detention for four months in 2016 but later released.
She did not attend Friday's hearing but in a statement read by her lawyer Erdal Dogan, Erdogan said her columns did not contain any violent element.
"Their political content is limited to human rights violations," she said, adding that the accusations based on her literary texts "trampled on the values of both law and literature".
Erdogan is the author of novels including "The City in Crimson Cloak" and "The Stone Building and Other Places" which are famed for their unflinching exploration of loss and trauma, and her detention had raised concerns worldwide.
For rights advocates, the trial was emblematic of a systematic crackdown by the government on freedom of expression, particularly after the failed coup.
A post-putsch purge by Turkish authorities targeted not just alleged backers of US-based preacher Fethullah Gulen -- blamed by Ankara for the coup plot -- but also opposition media and people accused of PKK ties.
Ankara however rejects the accusations of wide-scale rights violations and says the sweeping operations were aimed at keeping the state clean of Gulen's "virus".
In an 2018 interview with AFP in Germany, Erdogan said her country was sliding into fascism.
"The extent of things in Turkey is like Nazi Germany," she said. "I think it is a fascist regime. It is not yet 1940s Germany, but 1930s."
Erdogan's mother Mine Aydostlu appeared jubilant after the verdict.
"Believe me, I am very happy. I could not believe it. I was expecting this but still, I couldn't believe it," she told AFP outside Istanbul's main court.
"I asked many times if she was really acquitted. I could only believe it after I heard the word acquittal nine or 10 times."
After the travel ban against Erdogan was lifted in June 2017, she has largely lived in self-imposed exile in Europe and is currently in Berlin.
Her lawyer said she was abroad because she was suffering health problems as a result of her 2016 detention, and for a writing scholarship.
"She is not seeking asylum, she is abroad for a temporary period of time," he told AFP.
"She will not come to Turkey today but of course she will return. Turkey is her homeland."