The Qaedat al-Jihad fi Wadi al-Rafidain (The Foundation of Holy War in Mesopotamia) made the announcement in an internet statement, the authenticity of which could not be immediately verified.
"We, the al-Qaida in Iraq organisation, announce that the Egyptian ambassador has been kidnapped by our mujahidin and he is under their control," the statement, posted on a web forum, read.
The statement made no threat to kill the diplomat, Ihab al-Sherif, and did not present any demands. It said only that further information would be released later.
Al-Sherif was seized on Saturday in Baghdad.
Arab League Secretary-General Amr Moussa condemned al-Sherif's kidnapping and the attack on a Bahraini diplomat on Tuesday, saying they "serve the interests of those who try to sever Iraq's ties with its Arab surroundings".
"Such acts confuse the Arab public as it tries to understand what is going in Iraq," he said.
He said the presence of diplomatic missions in Baghdad show Arab nations' "genuine desire to continue contacts with all the Iraqi people. It is also an affirmation of the Arab identity of Iraq".
Amnesty International also condemned the attacks.
In a statement sent to Aljazeera.net, the rights organisation said the abduction of Egypt's ambassador to Iraq on Saturday, Tuesday morning's attempted assassination of Bahrain's envoy and the attack on the Pakistan ambassador's convoy, were an intensely worrying new trend in abuses by armed groups.
"The attacks on Arab and foreign diplomats in recent days appear to represent a new and worrying phase in the campaign by armed groups opposed to the Iraqi government and the presence of US and other foreign troops in Iraq," the statement said.
Amr Moussa: Such acts confuse
the Arab public
The statement accused the diplomats' abductors of preventing the Arab governments from developing appropriate ties with the new Iraqi leaders.
"Clearly, the aim of these groups is to deter Arab foreign governments from developing close relations with the new Iraqi administration and are seeking to ratchet up further their campaign of violence against all those associated with the new government," the statement said.
Aljazeera's correspondent in Cairo has learned that contacts between the Egyptian and Iraqi authorities are ongoing, and the latest information indicates that al-Sherif is well and has not been harmed.
The Egyptian cabinet has issued a statement expressing hope that the envoy will be released soon in order to resume his work as head of his country's diplomatic mission in Iraq.