Sudan's President Omar Hassan al-Bashir (Photo: Reuters)
Sudanese foreign ministry spokesman Al-Obeid Meruh told AFP, "The Sudanese government has ordered the Kenyan ambassador to leave the country within 72 hours."
"They have also ordered the Sudanese ambassador to leave Kenya and return to Khartoum," he added.
Bashir is wanted in The Hague-based ICC for alleged war crimes, crimes against humanity and genocide committed in Sudan's Darfur region, where the UN says at least 300,000 people have been killed in the eight-year conflict.
Kenya has ratified the ICC's founding Rome statute, which theoretically obliges it to execute the court's warrants, but it failed to arrest the Sudanese leader when he visited the country in August 2010.
After issuing the arrest warrant on Monday, the Kenyan high court judge said Bashir's arrest should be arranged by the Attorney General and the Minister for Internal Security "should he ever set foot in Kenya."
Bashir flew to Nairobi last year to attend a ceremony marking the adoption of Kenya's new constitution.
After leaving the country a free man, the Kenyan chapter of the International Commission of Jurists, an association of legal professionals that promotes human rights, approached the courts to issue a warrant.
"Bashir came in August and we filed [our suit] in October 2010. It was in response to his arrival here," George Kegoro, ICJ Kenya's executive director told AFP.
Just hours before announcing the expulsion of the Kenyan ambassador, Sudan's foreign ministry spokesman had said the arrest warrant was linked to internal political wranglings in Kenya and would not affect bilateral relations.
The African Union has on several occasions called on its members states not to arrest the Sudanese president, accusing the ICC of targeting only Africans and arguing that Bashir's arrest would hurt the peace process between Sudan and South Sudan.
Bashir took part in a regional summit in Malawi in mid-October after attending an investiture ceremony for Djibouti President Ismaël Omar Guelleh in May.
The Darfur conflict first erupted between non-Arab rebels and the Arab-dominated Khartoum regime in 2003.
Around 1.9 million people remain displaced in addition to the hundreds of thousands dead, according to UN estimates.
The Sudanese government puts the death toll at 10,000 and blames the continuing lack of security on tribal conflict, minority armed forces and banditry.
The ICC's chief prosecutor, Luis Moreno-Ocampo, accuses Bashir of having personally instructed his forces to annihilate the Fur, Masalit and Zaghawa ethnic groups in Darfur.