The group, which specialises in Pacific West Coast-style pizzas, is owned by Canadian husband and wife team Darren Atwater and Martha Gall.
The site at 122 Bethnal Green Road will be open all week from noon until 10pm, and mostly focus on takeaway orders, alongside a small 12-cover seating area.
As with the Clerkenwell kitchen, Wedge Issue Shoreditch will serve pizzas with three-day proofed dough, topped with a traditional Neapolitan-style sauce made with San Marzano tomatoes and mozzarella, which can be swapped for buffalo mozzarella on request.
Chef Malek Safsaf, who has worked across London and in Copenhagen, will oversee the kitchen.
Topping options include The London Fields, with crushed beef meatballs, ricotta cheese, fresh chilies and mozzarella; The Billingsgate, with anchovies, mushrooms, artichokes, capers, olives, and mozzarella; The Maribel, with spicy chorizo, ricotta cheese and mozzarella; and The Charlton, with chicken, feta, pesto, spinach, and mozzarella.
The menu also includes classic Italian pasta dishes such as spaghetti carbonara and penne arrabiata, simple salads, and desserts such as sticky toffee pudding and gluten free chocolate pudding.
Gluten-free bases will be available for the same price as usual bases, and the group also offers vegetarian and vegan toppings such as melting vegan cheese, vegan chorizo and vegan meatballs.
There will also be vegan chocolate pizza.
Atwater and Gall fell in love with authentic Pacific West Coast pizzerias on their travels between Vancouver and the US cities of Seattle and Portland, and opened the first Wedge Issue in 2016 after failing to find any similar pizza and beer joints in London after ten years of living there.