Initial reports from broadcaster N24 said that the 48-year-old female victim had been hospitalised in critical condition, but they later changed their report to say she had succumbed to her injuries at the crime scene.
A lawyer and another woman were also injured in the shooting before the gunman turned the gun to his head and killed himself.
The gunman, a professional chef, legally owned his firearm for sporting purposes, news agency DDP reported.
During a pause in legal proceedings regarding a family dispute over an inheritance, an argument broke out between seven family members, witnesses said. The family from the nearby city of Dingolfing had apparently been involved in years of legal wrangling, but the argument appeared to be resolved before court went back in session.
“From the trial itself and the chain of events, nothing seemed to induce this,” court spokesperson Karl Wörle said.
The shooting began shortly thereafter and people in the building that employs some 130 began to panic and barricade doors, news magazine Der Spiegel reported.
Court spokeswoman Elisabeth Waitzinger told the magazine that she could not explain how the situation escalated so quickly, though she did say that there were no weapon searches on civil cases at the court.
Police sealed off the building in the city of 63,000 residents just north of Munich, but the gunman was already dead by the time they arrived, the magazine said.
Meanwhile police are investigating the authenticity of a suicide note presented by one of the family members from the gunman on Tuesday afternoon. In the letter he writes of being terrorised by his family for years in legal proceedings.
The killing comes just four weeks after 17-year-old Tim Kretschmer took an unsecured nine-millimetre pistol from his father's bedroom on March 9 and killed 15 people at his former school in the Baden-Württemberg town of Winnenden. He later killed himself in a police pursuit.
The Bavarian State Premier Horst Seehofer called the Landshut incident an “incomprehensible act” and called for the state cabinet to strengthen weapon controls.
“It appears to me after all the information we've gathered in the last weeks, that weapons laws are a weak point,” he said.