Short answer
No. If your first stop is Madinah, you do not need ihram on the flight, even if you land in Jeddah and drive to Madinah. You enter ihram later at Dhul Hulayfah (Abyar Ali), the miqat of Madinah, when you set out for Makkah.
Ihram is required only of someone passing the miqat while heading to Makkah. A traveller whose real destination is Madinah does not need ihram on the way. When he leaves Madinah for Makkah, he should enter ihram at Dhul Hulayfah, and passing the last miqat on his route without ihram requires a dam.
The four schools agree on this.
Explanation
The miqats exist for people heading to the Haram of Makkah. Madinah is outside that Haram, so a pilgrim who flies straight to Madinah, or lands in Jeddah and goes directly to Madinah, does not owe ihram on that journey. The Prophet ﷺ named Dhul Hulayfah as the miqat for the people of Madinah and for those who pass through it, and the four schools agree on this.
- Madinah first, Makkah after: travel to Madinah in normal clothes. Before leaving for Makkah, bathe and change at your hotel, and make the intention at the mosque of Dhul Hulayfah (Abyar Ali), about 10 km from the Prophet's Mosque, or before your bus passes it.
- Makkah first, Madinah after: you enter ihram on the plane before the miqat, as explained in ihram when flying to Jeddah.
- Flying from Madinah to Jeddah: the flight passes the Madinah miqat area, so enter ihram before boarding or soon after take-off.
Your plan must be real. If you book a Jeddah arrival with the umrah as your first stop and only claim Madinah as a reason to skip ihram, the rule of the miqat applies to you. Visiting the Prophet's Mosque is not part of Hajj or umrah, but it is a great blessing; see Is visiting Madinah part of Hajj?.
The evidence
Sahih al-Bukhari 1526
Sahih... فهن لهن ولمن أتى عليهن من غير أهلهن ...
"They are for their own people and for those who come to them from elsewhere, intending Hajj or umrah."
In the same hadith Dhul Hulayfah is named as the miqat of the people of Madinah.
Where the ruling is recorded
- al-Hidaya, Kitab al-Hajj, section on the miqats. Ihram is due on someone who passes the miqat intending Makkah.
- Radd al-Muhtar (Ibn Abidin), Kitab al-Hajj, the miqats. A person heading to a place outside the Haram does not owe ihram at the miqat.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.