The US singer also confirmed they are called Sir Carter and Rumi – which had been rumoured after she and husband Jay-Z filed a trademark for the names.
The picture showed the 35-year-old mother-of-three and the twins draped in a purple floral sheet, while she wore a blue veil.
It clocked up more than two million likes on Instagram in an hour.
Beyonce wrote: “Sir Carter and Rumi 1 month today”, with a string of emojis of prayer hands and a woman, man, little girl and two babies.
As well as the twins, Beyonce and rapper Jay-Z are also parents to five-year-old daughter, Blue Ivy.
The style of the image, in which Beyonce stands in a garden barefoot in front of a floral archway, echoes the photoshoot she used to announce her pregnancy on the network. That post, in February, became the most-liked in the history of Instagram.