The primary target organ of coronavirus disease 2019 (COVID-19) infection is the respiratory tract. Currently, there is limited information on the ability of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to infect and regulate innate immunity in human immune cells and lung epithelial cells. Here, we compared the ability of four Finnish isolates of SARS-CoV-2 from COVID-19 patients to replicate and induce interferons (IFNs) and other cytokines in different human cells. All isolates failed to replicate in dendritic cells, macrophages, monocytes, and lymphocytes, and no induction of cytokine gene expression was seen. However, most of the isolates replicated in Calu-3 cells, and they readily induced type I and type III IFN gene expression. The hCoV-19/Finland/FIN-25/2020 isolate, originating from a traveler from Milan in March 2020, showed better ability to replicate and induce IFN and inflammatory responses in Calu-3 cells than other isolates of SARS-CoV-2. Our data increase the knowledge on the pathogenesis and antiviral mechanisms of SARS-CoV-2 infection in human cell systems. IMPORTANCE With the rapid spread of the coronavirus disease 2019 (COVID-19) pandemic, information on the replication of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and regulation of innate immunity in human immune cells and lung epithelial cells is needed. In the present study, we show that SARS-CoV-2 failed to productively infect human immune cells, but different isolates of SARS-CoV-2 showed differential ability to replicate and regulate innate interferon responses in human lung epithelial Calu-3 cells. These findings will open up the way for further studies on the mechanisms of pathogenesis of SARS-CoV-2 in human cells.