A spokesman for Attorney General John Larkin’s office confirmed that the matter had been referred to the region’s senior law officer by Lord Chief Justice Declan Morgan.
Mr Larkin is to investigate whether the comments represent a breach of contempt of court laws.
Meanwhile, two people have been questioned by police in the North in relation to naming the complainant in the case online.
Ulster and Ireland stars Paddy Jackson, aged 26, and Stuart Olding, aged 25, were acquitted of rape on Wednesday following a nine-week trial at Belfast Crown Court.
Mr Jackson was also found not guilty of sexual assault when the jury of eight men and three women returned unanimous verdicts after three hours and 45 minutes of deliberation.
Two other men were acquitted of lesser charges related to the same incident.
Blane McIlroy, aged 26, was acquitted of exposure while Rory Harrison, 25, was found not guilty of perverting the course of justice and withholding information.
Under law, jurors are not permitted to disclose details of their deliberations in any trial.
The remarks from the juror appeared hours after the unanimous not guilty verdicts were delivered below a story on the case on the website Broadsheet.ie.
The involvement of the attorney general was first reported by the Irish Times yesterday.
Police said they were aware of the comments.
“We are aware of comments made on a social media platform,” a Police Service of Northern Ireland (PSNI) spokesman said.
The PSNI has also quizzed two people about alleged breaches of the complainant’s right to anonymity.
“There is an ongoing police investigation and two people have been interviewed in relation to an offence under section five of the Sexual Offences Amendment Act 1992,” said the PSNI spokesman.
“Two files have been forwarded to the Public Prosecution Service for consideration.”
The high-profile trial, which ran for 42 days, generated an unprecedented level of public attention and prompted calls from Mr Jackson’s defence solicitor for a crackdown on social media comment during criminal proceedings.
It has also renewed the debate on whether defendants in rape trials should also be entitled to anonymity, with their names only being revealed if they are convicted.
In another post-trial development, a number of media outlets are challenging reporting restrictions still placed on the case.
Restrictions preventing reporting on legal exchanges that take place in the absence of the jury usually fall away once the case is over, as the issue of prejudicing jurors is no longer relevant.
A number of outlets that covered the marathon trial are now seeking to get ongoing restrictions imposed by Judge Patricia Smyth lifted.
While the issue has been listed for a mention hearing before the judge on April 25, lawyers for press and broadcasters are endeavouring to have the matter dealt with next week.