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 Any significant medical condition, laboratory value or other illness that in the investigator's opinion would interfere or prevent safe participation in the study History of a splenectomy, lung transplant or lung lobectomy Concurrent participation in another clinical trial involving therapeutic interventions (observational study participation is acceptable)