Despite intense investigation, the pathogenesis of COVID-19 and the newly defined long COVID-19 syndrome are not fully understood. Increasing evidence has been provided of metabolic alterations characterizing this group of disorders, with particular relevance of an activated tryptophan/kynurenine pathway as described in this review. Recent histological studies have documented that, in COVID-19 patients, indoleamine 2,3-dioxygenase (IDO) enzymes are differentially expressed in the pulmonary blood vessels, i.e., IDO1 prevails in early/mild pneumonia and in lung tissues from patients suffering from long COVID-19, whereas IDO2 is predominant in severe/fatal cases. We hypothesize that IDO1 is necessary for a correct control of the vascular tone of pulmonary vessels, and its deficiency in COVID-19 might be related to the syndrome’s evolution toward vascular dysfunction. The complexity of this scenario is discussed in light of possible therapeutic manipulations of the tryptophan/kynurenine pathway in COVID-19 and post-acute COVID-19 syndromes.