Several events in an animal’s life are considered stressful. Among them, the most studied and significant are transportation, weaning, and adaptation to climate change. Moreover, other events, such as the separation from the dam, moving from the original farm to another, management practices, such as regrouping with other animals, and new hierarchical conditions, represent routine conditions in the bovine’s life, which can influence the animal’s homeostasis. The purpose of this study is to evaluate the changes in blood parameters of 45 calves introduced into a new environment from their original farms. Blood samples were collected upon arrival at a genetic center (T1), 7 (T2), 30 (T3), and 120 (T4) days after arrival. Blood count, protein electrophoresis, clinical chemistry, and innate immunity parameters were performed on the samples. Significant alterations in some clinical chemistry parameters were related to liver function in the serum protein and the values of IL-6 and TNF-α; the main cytokines mediating the stress response emerged from the results. The evidence indicates the mild response to adaptation stress by calves raised in close association with people after their introduction into a new environment.