Shareena Clanton alleged "multiple racist traumas" during her time on the show in an Instagram post on Monday.
A day later, former Neighbours actor Meyne Wyatt said he too had experienced racism on set in a tweet.
The actors, both Australians of indigenous descent, said they heard other cast members use racist slurs.
"It's been lonely, triggering and traumatising to work in such a culturally unsafe space," wrote Ms Clanton, who has guest starred in yet-to-be-aired episodes of Neighbours.
In response to Ms Clanton's allegations, the show's producer, Fremantle Media, said it would do more to promote inclusion.
"Neighbours strives to be a platform for diversity and inclusion on-screen and off-screen," a spokesperson for Fremantle Media told the BBC. "Our quest is always to continue to grow and develop in this area and we acknowledge that this is an evolving process."
First broadcast in 1985, Neighbours follows the lives of the residents of Ramsay Street, in a fictional suburb of Melbourne, Victoria. The soap was a launch pad for numerous pop and Hollywood stars, including Kylie Minogue and Russell Crowe.
But the soap has been criticised for failing to reflect Australia's ethnic diversity in its casting of actors.
Mr Wyatt was the first indigenous actor to be added to the main cast when he appeared on the show from 2014 to 2016.
A spokesperson for Channel 5, which airs the soap in the UK, said it "condemns racism and takes all allegations of discrimination seriously".