The bar's drinks list features a cocktail menu that uses ingredients such as cardamom, lemongrass, ginger and sweet spices.
Highlights include coriander & lychee daquiri with chairman's reserve rum, fresh Lime, lychee juice and coriander leaves and a chai tea martini made with fresh chai, stolinaycha vodka and apricot brandy.
A Lassi menu will also be available at the new venue.
Dan Thomson, manager of Zenna, said: "We wanted to create a contemporary bar that was still true to its Indian heritage and provide a chic and welcoming space in the midst of Soho.
"Zenna Bar is London's first ever Indian cocktail bar and the carefully thought through flavours, recipes and ingredients used in the drinks list, as well as the authentic canapés make it a unique offering in the capital."