New South Wales Waratahs player Folau, an Evangelical Christian, made similar comments last April.
"Rugby Australia is aware of a post made by Israel Folau on his Instagram account this afternoon," Australian rugby's governing body said in a statement on Wednesday.
"The content within the post is unacceptable. It does not represent the values of the sport and is disrespectful to members of the Rugby community.
"The Rugby Australia Integrity Unit has been engaged on the matter tonight."
Folau, 30, also took to Twitter to condemn a landmark decision on Wednesday by the Australian state of Tasmania to make it legally optional to list gender on birth certificates.
In February, Folau extended his Wallabies deal until 2022 ahead of this year's World Cup, although contract negotiations were complicated by his conservative religious views.
Folau faced no sanctions in April last year for anti-gay comments after RA said it accepted his position that he did not mean to harm the game..
Folau had offered to walk away from the sport if RA found itself in an untenable position with sponsors and fans.
(Reporting by Hardik Vyas in Bengaluru; Editing by Ken Ferris)
