The weapon is an AR-15-pattern rifle, three anonymous government sources told the outlet.
A second weapon found at the scene — a handgun — was purchased on May 29.
Tulsa police have said both weapons appear to have been used in the rampage, which killed four people in an orthopedic office on the second floor of the Natalie Medical Building at St. Francis Hospital.
Police have not yet identified the gunman, who died of an apparent self-inflicted gunshot wound.
Authorities executed a search warrant at a home in Muskogee, some 45 miles southeast of Tulsa, in connection with the shooting, Tulsa police said.
Police had initially responded to a report of a man inside the building with a rifle and a handgun before it escalated into an active shooter situation, cops said.
They arrived in three minutes and made contact with the shooter immediately.
According to Tulsa police, the scene was limited to the second floor of the building, part of which included the orthopedic office.
The Natalie building also houses an outpatient surgery center and a breast health center.
Tulsa Police Department Capt. Richard Meulenberg described the scene at the medical facility as “catastrophic.”