In his article, Dr Sentamu said the world could no longer remain "inactive" in the face of a growing humanitarian crisis.
He said a power-sharing deal between Mr Mugabe and the opposition Movement for Democratic Change was "now dead".
"The time has come for Robert Mugabe to answer for his crimes against humanity, against his countrymen and women and for justice to be done," Dr Sentamu wrote.
"The winds of change that once brought hope to Zimbabwe and its neighbours have become a hurricane of destruction with the outbreak of cholera, destitution, starvation and systemic abuse of power by the state.
"Robert Mugabe and his henchmen must now take their rightful place in The Hague and answer for their actions."
In December 2007, Dr Sentamu cut up his dog collar live on the BBC's Andrew Marr Show and vowed not to wear another until Zimbabwe saw a change in regime.
Gordon Brown: 'The states around Zimbabwe are getting increasingly angry'
The Archbishop has joined a growing list of international leaders in condemning Mr Mugabe.
Mr Brown said he had "been in close contact with African leaders to press for stronger action to give the Zimbabwean people the government they deserve".
The prime minister did not explicitly call for Mr Mugabe to step down, but said world leaders should stand together to defend human rights and democracy in Zimbabwe.
He added: "The people of Zimbabwe voted for a better future. It is our duty to support that aspiration."
He also said he hoped the United Nations Security Council would meet "urgently" to consider the country's plight.
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