The 12 escapees are Algerians, Libyans and Moroccans. One of them was found injured later Wednesday and admitted to hospital, deputy state prosecutor Thomas Bernard said.
According to local media, the men used a makeshift hook to force open a gate on Wednesday evening before fleeing over a wall surrounding the center in Metz.
"A judicial inquiry is underway" and "measures are being taken to find the individuals," the government's regional authority said.
Police are studying video surveillance cameras for clues about where the others were headed, he added.
Border police declined to comment on the escape from the center, which can hold nearly 100 people who are awaiting deportation after entering the country illegally.
In recent years France has tried to crack down on illegal immigration by making it easier to deport people whose asylum claims are rejected, while also restricting public aid for those seeking residency.