Louise Mushikiwabo, Rwanda's foreign minister called the arrest "an outrage".
Gen Karake is also accused of ordering the killing of three Spanish nationals working for Medicos del Mundo.
'Contested vigorously'
In 2008, a Spanish judge indicted him for alleged war crimes along with 39 other current or former high-ranking Rwandan military officials.
He was arrested by Metropolitan police officers under the European Arrest Warrant.
But the Rwandan government is said to be puzzled by the timing of Gen Karake's arrest, as he had travelled to the UK several times since the indictment was issued.
Williams Nkurunziza, Rwanda's High Commissioner to the UK, called the arrest "an insult".
"Any suggestion that any of our 40 leaders are guilty of crimes against humanity is an insult to our collective conscience."
Human Rights Watch reported that in their drive for military victory and to control the population, the RPF killed thousands, including government troops, members of the militia and some civilians in numerous executions and massacres.
Rwanda protest over spy chief arrest
Some 200 people gathered outside the British High Commission in Rwanda to protest at the arrest of intelligence chief Karenzi Karake in London.
Gen Karake, 54, was detained at Heathrow Airport on Saturday, accused of ordering massacres in the wake of the 1994 Rwanda genocide.
Protestors have threatened not to end the demonstration in the capital, Kigali, until the general is released.
The Rwandan government has branded the arrest an "outrage".
Louise Mushikiwabo, Rwanda's Foreign Minister condemned Gen Karake's detention on Tuesday, saying that "Western solidarity in demeaning Africans is unacceptable".
"We are here to stand in solidarity with our hero, who was among the people who stopped genocide in this country,'' Herbert Muhire, a protest leader told The Associated Press news agency.
William Gelling, the UK's High Commissioner to Rwanda, addressed the crowd briefly.
"All I can say is that this was a legal decision as you understand, on behalf of the Spanish legal authorities.
"The UK is a very close partner with Rwanda,''
