Fiqh-us-Sunnah Volume 3, Zakaat and Fasting, Fiqh 3.156A.

If someone makes a vow to perform i’tikaf in the Masjid alHaram (in Makkah), the Prophet’s Mosque (in Madinah), or in the Aqsa Mosque (in Jerusalem), he is to fulfil his vow, as the Prophet said: “One should not undertake journeys except to three mosques: the Masjid al-Haram, the Aqsa mosque, or this mosque.”

If someone vows to perform i’tikaf in another mosque, it is not obligatory on him to fulfil it and he may perform that i’tikaf in any mosque, for Allah did not specify any particular place for His worship, and there is no superiority of one mosque over another (with the exception of the three mosques mentioned earlier). It has been confirmed that the Prophet said: “A prayer in my mosque is superior to one thousand prayers in any other mosque but the Masjid alHaram, and a prayer in that mosque is superior to a prayer in my mosque by one hundred prayers.”

Thus, if someone makes a vow to perform i’tikaf in the Prophet’s mosque, he may fulfil it in the Masjid al-Haram since that one is superior to the Prophet’s mosque.