The sandwich giant currently has seven of the stores - six in London locations including Soho and Canary Wharf, and just one outside the capital, in Manchester's Deansgate.
The new Veggie Prets will bring the UK total to 14 - with all but one of the stores in London.
In addition to announcing the new meat-free outlets, the chain has recently had a major revamp of the menu at Veggie Pret.
It launched 15 new vegan menu items, including Poké Bowls, Smoothie Bowls, and Buddha Bowls, in a bid to tap into the growing demand for plant-based food.
Pret A Manger bought rival EAT stores in a £60 million deal announced last year.
The chain had planned to turn all the acquired EAT sites into Veggie Prets, but has appeared to scale back those plans for now.
Confirming the new stores, a Pret spokesperson said: "We're pleased to confirm that we are aiming to have 14 Veggie Pret shops open by summer 2020."