This is Masashi Kishimoto's manga, Karakuri. It was created before Naruto and was collected in Naruto: The Official Premium Fanbook.

In order to combat a deadly virus, an implant was made that is transplanted into a human being's nervous system. Unfortunately, this implant technology was also used by the less scrupulous to create human weapons, blood-red eyed creatures referred to as "Roido". To cope with this threat the defense agency has created the Karakuri unit, an elite unit whose human members are monitored by small talking animals. As Kiru the karakuri goes to visit his friends Koten and Koron while on leave, he's going to learn that there are no days off against the Roido!