Protais Zigiranyirazo has spent eight-and-half years in prison
The UN tribunal hearing cases from the 1994 Rwandan genocide has freed a man who had been sentenced to 22 years.
Protais Zigiranyirazo, the brother-in-law of ex-Rwandan President Juvenal Habyarimana, had been found guilty of organising a massacre of 1,000 people.
But the appeals court judge said there had been serious errors in his trial and his conviction in 2008 violated "the most basic principles of justice".
Reporters say Mr Zigiranyirazo looked stunned and relieved by the ruling.
"God is great and justice has been done. I am very happy," he told the BBC's Great Lakes service.
Mr Habyarimana's plane was shot down on 6 April, 1994, sparking the 100-day massacres in which an estimated 800,000 ethnic Tutsis and moderate Hutus were killed.
Mr Zigiranyirazo was accused of leading a convoy that attacked Tutsis who were seeking refuge on a hill a few days after the genocide began.
But Judge Theodor Meron said the trial judgment had "seriously erred in its handling of the evidence", AP news agency reports.
Mr Zigiranyirazo told the BBC he would be seeking compensation for the eight-and-half years he had already spent in detention.
Rwanda's justice minister told the BBC the government was very unhappy about the decision, but could not reverse the judgement
The International Criminal Tribunal for Rwanda (ICTR), based in Tanzania, was set up to try high-profile genocide cases.
Meanwhile, the US ambassador for war crimes, Stephen Rapp, has called on the Kenyan authorities to arrest a key genocide suspect.
The BBC's East Africa correspondent Will Ross says officials at the ICTR have long maintained that Felicien Kabuga is hiding in Kenya and that the Nairobi government is protecting him.
Mr Rapp said he had received fresh reports that Mr Kabuga was in Kenya.
"The latest response of government authorities is, 'Oh he's left.' The ICTR says if he's left show us the evidence. And they say, 'Well we're still looking for that evidence,'" Mr Rapp said.
"If you are still looking for the evidence you cannot honestly say that he has left," he said.
The calls for Hutu people to exterminate the Tutsis during the genocide were broadcast over Radio Mille Collines, which was headed by Mr Kabuga, a wealthy businessman.