Folau was on Tuesday found to have committed a "high-level breach" of his RA contract after a three-day code of conduct hearing regarding his homophobic social posts in April.
"Asics is dedicated to sport and its healthy contribution to society", a company statement read.
Castle said Folau was warned "formally and repeatedly" about the expectations on him as a player, following similar social media posts from previous year.
Asics is now the second sponsor to abandon Folau due to his anti-LGBT posts-Land Rover withdrew a luxury vehicle issued to the player in April 2018, after he prompted outrage by saying gay people were going to hell "unless they repent of their sins".
The 30-year-old devout Christian posted on Instagram that "hell awaits" for "drunks, homosexuals, adulterers, liars, fornicators, thieves, atheists, idolators".
Rugby Australia said it had formally warned Folau against making inflammatory social media comments last year before awarding him his new four-year, $4 million contract.
The disciplinary panel said it will "take further written submissions from the parties to consider the matter of sanction".
What is understood to have been factored in is if Folau escapes, and then makes another inflammatory post, he and RA will be forced to head down another costly code of conduct hearing in future.More news: Woman pulls alligator from her pants during traffic stop
The head of Rugby Australia's biggest sponsor says he is "quite happy" with the organisation's tough ruling against Israel Folau.
"Israel Folau, with my support and the support of millions of Australians, will take this fight every inch of the way", Jones said.
In a column for Players Voice, Rathbone wrote: "I'd like to ask Alan if he believes his employer, commercial radio station, 2GB, is obligated to continue employing him regardless of his speech?
In many ways it was very, very sad", Jones said.
Sportswear brand Asics dumped Israel Folau as a brand ambassador on Wednesday (8 May).
Both Folau and Rugby Australia can lodge an appeal within 72 hours of the sanction decision.
RA revealed its intention to sack Folau for his latest homophobic quote, which came after a similar post on social media past year sparked controversy.
"What this is causing, vis-a-vis a divide amongst fans amongst just the game in general, the other sports must be laughing at us", he said. "I think our, and my, history on that is that you go too tight on stuff, there'll be stuff that sits outside and you'll have other, broader problems down the track", McLachlan said.
That message came after Jones said the "Orwellian treatment" of the rugby icon, combined with various recent attacks on politicians, painted a grim picture of the state of Australia.