James Michael Meyer, 72, was being held on $150,000 in Dallas County Jail as of Friday.
Authorities said police officers were dispatched to Meyer's home just after 7 a.m. There, a body was found lying face down in a park behind the property, The Dallas Morning News reported.
Meyers told police he was awakened by a noise around 5 a.m. and saw someone trying to break into his storage shed with a pickax. He grabbed his gun, came out the home and yelled at the alleged burglar.
He said he shot the person, who was coming toward him. The burglar dropped the pickax and ran toward the park, Meyers said.
He didn't know whether he hit the person so he went back to bed, an arrest warrant affidavit said. After sunrise, he said he saw the person lying on the ground.
He told investigators he threw the spent shell casings in the trash. Court documents said Meyers refused to answer questions from a 911 dispatcher, saying only that he was defending himself and that medical assistance was needed.