The gunman, who later got into a shootout with police, also was in critical condition after shooting himself, said Dallas police spokesman, Sr. Cpl. Lt. Kevin Janse.
The shootings happened just before 11 a.m. in the 15-story Four Forest high-rise office building, which houses the United Texas Bank and other businesses near the intersection of U.S. 75 and Interstate 635.
The gunman walked into a financial services office on the third floor and opened fire on the father and his son, who apparently had an ongoing dispute with the suspect, Janse said.
After three police officers arrived on the scene, the man came out of the office and pointed his gun at them, Janse said. Police fired several shots without hitting him, and the man went back into the office where he shot himself, he said. He was in critical condition at the nearby Medical City Dallas hospital.
The 63-year-old man was shot in the legs and his 39-year-old son was shot in the neck, and both were in stable condition at Medical City Dallas, Janse said.
During the shootings, the building was on lockdown and about 16 people took refuge in the vaults in the bank on the building's first floor.
"The building has announced we should stay in here until they let us know otherwise," bank employee Linda Farley told WFAA-TV of Dallas and Fort Worth by telephone from the vault. "Everybody is a little scared."
Police did not immediately release more information including the identities of the alleged gunman and the father and son.