Given a left Noetherian ring R, we give a necessary and sufficient condition in order that a complex of R-modules be DG-injective. Using this result we prove that if (Ki)i∈I is family of DG-injective complexes of left R-modules and K is the 1-product of (Ki)i∈I (i.e. Kℵ ⊂ i I Ki is such that, for each n, Kn ⊂
i∈I Kn/i consists of all (xi)i∈I such that {i | xi xi=/=0} is at most
countable), then K is DG-injective.