Inclusion Criteria:  Has had prior laboratory-confirmed SARS-CoV-2 infection as determined by an approved polymerase chain reaction (PCR) or an approved antigen test of any specimen Has had a recent (within a week) negative SARS-CoV-2 test (an approved PCR or antigen test) Has had at least moderate or severe post-COVID-19 pulmonary symptoms for at least 3 months which have resulted in reduced physical functioning compared to pre-COVID-19 status Willing to follow contraception guidelines  Exclusion Criteria:  Clinically improving pulmonary status over the month prior to screening Undergone a previous stem cell infusion unrelated to this trial Pregnant or breast feeding or planning for either during the study Suspected uncontrolled active bacterial, fungal, viral, or other infection History of a splenectomy, lung transplant or lung lobectomy Concurrent participation in another clinical trial involving therapeutic interventions (observational study participation is acceptable)