Tanya Zuckerbrot -- a registered dietician and Instagram influencer -- is suing Instagram influencer Emily Gellis claiming that beginning in July she's made more than 4,500 false claims over a 75-day period that her F-Factor diet causes physical harm ... and in some cases, death, this according to docs obtained by TMZ.

In docs, Zuckerbrot says she created protein powders and protein bars in 2017 touting her F-Factor diet, which she describes as a "liberating and sustainable approach to weight loss and optimal health based on scientifically proven fiber-rich nutrition."

Zuckerbrot claims Gellis has 750 minutes of video trashing the diet. She says Gellis falsely claimed F-Factor products caused a woman to miscarry a pregnancy. Zuckerbrot also claims Gellis falsely claimed the products contained unsafe levels of arsenic. According to the suit,  Gellis also falsely claimed someone died from using the product.

Zuckerbrot's got a laundry list of things she claims Gellis -- who boasts 208k followers on IG -- said about her and the diet products, including accusing Zuckerbrot of "selling f***ing packaged poison" and “profit[ing] off this cult-like mentality.”

She claims the company was generating over $1 million a month in revenue ... until Emily's "illegal, abusive and harassing social media misconduct," which Zuckerbrot says caused "devastating financial damages and enormous emotional distress."