The authenticity of the statement could not immediately be verified.
The blast on Thursday evening, apparently caused by a booby-trapped motorcycle, was the first attack against foreigners in the capital in more than seven years and came amid upheaval in Egypt's political scene.
The internet statement said the attack was perpetrated "to avenge our brothers, martyrs of injustice, and detainees" and to prove to Egyptian President Husni Mubarak who "speaks of sleeper cells that there are also active mujahidin working against him and his likes".
Egyptian Tourism Minister Ahmad al-Maghrabi said a Frenchwoman and a US national had been killed in the blast, while the third victim had not yet been identified.
He said three Americans, two French and four Egyptians were also being treated at hospital. One of the French nationals was in a serious condition while the other wounded were stable, he added.