The actor and streaming giant are being sued over "Down To Earth With Zac Efron" by a company called Down To Earth Organics, which claims the Netflix travel show is hurting their biz.

According to the lawsuit, obtained by TMZ, DTE claims they locked down the rights to "Down To Earth" for media and entertainment purposes well before Zac and Netflix premiered their show.

DTE says the Netflix series, which follows Zac around the globe to find healthy, sustainable ways to live, is trying to create a new "Down To Earth" wellness brand ... and the company says it's hurting their bottom line by confusing customers.

What's more, DTE says the Netflix series' advice on wellness "has been widely ridiculed" and is pushing "damaging false nutrition claims." ... and they're not fans of Zac using the show to cross-promote Nature Valley snack bars on social media, because DTE says they offer their own healthy snacks with the trademark.

DTE is going after Zac and Netflix for damages ... and they want an injunction prohibiting Zac and Netflix from infringing on their "Down To Earth" trademarks.