Studying the dynamics changes of neutrophils during innate immune response in coronavirus 2019 (COVID-19) can help understand the pathogenesis of this disease. The aim of the study was to assess the usefulness of new neutrophil activation parameters: Immature Granulocyte (IG), Neutrophil Reactivity Intensity (NEUT-RI), Neutrophil Granularity Intensity (NEUT-GI), and data relating to granularity, activity, and neutrophil volume (NE-WX, NE-WY, NE-WZ) available in hematology analyzers to distinguish convalescent patients from patients with active SARS-CoV-2 infection and healthy controls (HC). The study group consisted of 79 patients with a confirmed positive RT-PCR test for SARS-CoV2 infection, 71 convalescent patients, and 20 HC. We observed leukopenia with neutrophilia in patients with active infection compared to convalescents and HC. The IG median absolute count was higher in convalescent patients than in COVID-19 and HC (respectively, 0.08 vs. 0.03 vs. 0.02, p < 0.0001). The value of the NEUT-RI parameter was the highest in HC and the lowest in convalescents (48.3 vs. 43.7, p < 0.0001). We observed the highest proportion of NE-WX, NE-WY, and NE-WZ parameters in HC, without differences between the COVID-19 and convalescent groups. New neutrophil parameters can be useful tools to assess neutrophils’ activity and functionalities in the immune response during infection and recovery from COVID-19 disease.