The man and his wife were in the court in the city of Reggio Emilia as part of separation proceedings when he pulled out a gun and pointed it at his wife and her brother, then started shooting randomly, police said.
"He was shooting like crazy at everybody," officer Antonio Turi said.
The wife was taken to a hospital, where she was declared clinically dead, Italian media reported. Her brother died at the scene.
A police officer and the woman's lawyer also were injured, but not seriously, police said.
The ANSA news agency identified the man as Klirim Fejzo, his wife as Vyosa Demcolli and her brother as Arjan Demcolli, all Albanians.
Police were investigating how the man managed to carry a weapon inside the courtroom in Reggio Emilia, a city about 75 kilometers (47 miles) northwest of Bologna.