The defendant, who has not been named, was accused of sharing the videos on social media while pretending to be an ex-girlfriend accusing him of infidelity.
The release of the videos sparked a separate police investigation into the Nottingham Forest striker over whether the sexual encounters were filmed illegally without consent.
Hwang has denied the allegations and prosecutors have yet to clear or formally charge him.
The sister-in-law posted the videos "knowing it would be disseminated indiscriminately", the Seoul Central District Court said in a verdict, Yonhap news agency reported.
"The content has been widely distributed in and out of South Korea... the nature of her crime is very serious," the court said.
The three-year sentence was a year less than prosecutors had demanded.
The defendant's acknowledgement of the crime and Hwang's plea for leniency were taken into consideration, the court said.
"I have caused great harm to the victims and I sincerely regret what I have done," the defendant said in her final testimony.
The 31-year-old Hwang, who is on loan from Forest at Turkish club Alanyaspor, scored in a World Cup qualifier against Singapore in November.
But the Korea Football Association have since suspended him from the national squad pending the outcome of the investigation into the alleged illegal filming.
The suspension kept him out of the Asian Cup in Qatar.
Hwang has scored 19 goals in 62 appearances for South Korea.