The US singer complained the virtual assistant was pronouncing her surname wrong.
"I called the head of Apple, Tim Cook, and he delightfully agreed to have Siri change the pronunciation of my name, finally," she said on Weekend Edition.
Streisand said the second syllable of her name should be pronounced with "a soft S, like sand on the beach".
Siri currently pronounces the singer's name as "StreiZAND". The next Apple update is due on 30 September.
"So let's see if that happens, because I will be thrilled," Streisand told the US show on Saturday.
The singer is currently on tour for her new album, Encore: Movie Partners Sing Broadway.
In 2014, Streisand created US chart history by becoming the first artist to score number one albums in each of the last six decades.
She is one of just a few to have won all four major US entertainment awards - an Oscar, Emmy, Grammy and an honorary Tony.
Streisand has also enjoyed an illustrious film career which began with 1968's Funny Girl, for which she won an Oscar.
Her other films include The Way We Were, What's Up, Doc? and the Meet the Parents sequel, Meet the Fockers.
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A tweak to Siri's pronunciation of Barbra Streisand's name will be heading to Apple products soon.