The Frankfurt regional court also convicted Taha Al-J, an Iraqi citizen whose full last name was not released because of privacy rules, of crimes against humanity, war crimes and bodily harm resulting in death.

The 29-year-old was sentenced to life imprisonment and ordered to pay the girl's mother 50,000 euros ($A80,000).

Presiding judge Christoph Koller said it was the first genocide conviction worldwide over a person's role in the systematic persecution by IS of the Yazidi religious minority.

The judges concluded Al-J acted with the intention of eradicating Yazidis, thereby constituting genocide.

Lawyers for the defendant had denied the allegations made against their client, who briefly fainted as the verdict was read out on Tuesday.

His German wife was sentenced last month to 10 years in prison over the girl's death.

The girl's mother, who survived captivity, testified at both trials and took part as a co-plaintiff.

"This is the moment Yazidis have been waiting for," said lawyer Amal Clooney, who acted for the mother.

"To finally hear a judge, after seven years, declare that what they suffered was genocide. To watch a man face justice for killing a Yazidi girl - because she was Yazidi."

The United Nations has called the IS assault on the Yazidis' ancestral homeland in northern Iraq in 2014 a genocide, saying the Yazidis' 400,000-strong community "had all been displaced, captured or killed".

Of the thousands captured by IS, boys were forced to fight for the extremists, men were executed if they did not convert to Islam and women and girls were sold into slavery.

According to German prosecutors, Al-J bought a Yazidi woman and her five-year-old daughter, Reda, as slaves at an IS base in Syria in 2015.

The two had been taken as prisoners by the militants from the northern Iraqi town of Kocho in August 2014 and had already been "sold and resold several times".

The defendant took the woman and her daughter to his household in the Iraqi city of Fallujah and forced them to "keep house and to live according to strict Islamic rules", while giving them insufficient food and beating them regularly to punish them, according to the indictment.

Prosecutors allege that towards the end of 2015, Al-J chained the girl to the bars of a window in the open sun on a day when it reached 50C and she died from the punishment.

The punishment was allegedly carried out because the five-year-old had wet the bed.

Al-J was arrested in Greece two years ago and extradited to Germany.

German authorities took on the case under the principle of universal jurisdiction, which allows the country to try particularly serious crimes even if they were committed elsewhere.

Australian Associated Press