She went on to call for Germany to arm Kurds in northern Iraq fighting the Islamists. "They desperately need better equipment," she said.
Isis has carved out a caliphate in huge swathes of northern Iraq and Syria over the last few months.
The terror group was accused of ethnic cleansing after the United Nations said on Sunday that the Islamists had killed 670 prisoners in Mosul.
UN High Commissioner for Human Rights Navi Pillay said: “Grave, horrific human rights violations are being committed daily by ISIL and associated armed groups.
“They are systematically targeting men, women and children based on their ethnic, religious or sectarian affiliation and are ruthlessly carrying out widespread ethnic and religious cleansing in the areas under their control. Such persecution would amount to crimes against humanity.”
By describing Isis massacres in the Middle East as “genocide”, Merkel has gone further than other western leaders.
When he announced airstrikes against the terror group at the start of August, US President Barack Obama said the US wanted to “prevent a potential act of genocide”.
Merkel added in the interview that Germany was in the process of delivering 100 tonnes of humanitarian aid to northern Iraq.
So far German support for the Kurds has been limited to food and medical supplies, but the German Parliament is set to decide on Monday whether to deliver weapons to the Kurds, something the ruling coalition government has called for.
But German public opinion has so far opposed sending weapons to the Kurds. A poll published last week said 63 percent of Germans were against shipping arms to Kurdish forces.