The refrigerated meat machine is the fifth to open in France, but the first in the capital. Laetitia Lafaye, the first French butcher to install a meat vending machine, in the southwestern town of Sainte-Catherine, said the idea came from Germany, where there are hundreds of such machines.
Last year a cheesemonger in the eastern town of Pontarlier installed an automatic cheese distributor.
Paris got its first 24-hour baguette vending machine in 2011. Since then, hundreds more have been installed across the country.
But the spread of the machines is proving controversial. Traditionalists say they will lead to the demise of craft butchers, bakers and cheese shops.
Emmanuel Gripon, from the French Bakers' Federation, said: "It's contributing to the desertification of the countryside and it harms the social life of communities."
However, many people welcome the convenience they offer. Francois Joly, who lives near L'Ami Txulette, said: "At first you think it's strange, but then you realise it might be a good way to buy meat if you work late and feel like a steak when you get home."