Officials said the attack was in retaliation to a controversial headscarf ban in the country, and underscores political tensions between the secular establishment and the Islamist government.
Judge Mustafa Yucel Ozbilgin, who was hit in the head, died in intensive care after six hours of brain surgery, doctors said.
Chamber President Mustafa Birden was also seriously hurt but his life is out of danger and the three other judges suffered lighter injuries.
The attacker was identified as lawyer Alpaslan Aslan, 29, who was arrested straight after the shootings.
He reportedly chanted "God is Great!" as he fired his weapon, according to media reports, and said he wanted to punish the headscarf ruling.
Headscarves are banned from being worn in public institutions and universities, however the ruling Justice and Development Party (AKP) opposes this and has often criticised court rulings upholding the ban.
Justice Birden had been criticised for a February decision barring the promotion of a teacher who wore the scarf outside of work.
Prime Minister Recep Tayyip Erdogan angrily rejected any ties between the incident and AKP's campaign to lift the headscarf ban.
"It is very ugly to draw such links," he said.
Deniz Baykal, leader of the social democratic main opposition Republican People's Party, also lashed out at the government.
"Turkey is being dragged in a very dangerous direction," he said. "Those behind the forces that have brought us to this point should come to their senses."
Media reports said the assailant was armed with an Austrian-made Glock automatic pistol, which can pass through metal detectors without setting off alarms.