That is certainly not true. As Mohammad was NOT the descendant of Ishmael.
The following traditions demonstrate that even Muslims were unable to link Muhammad's lineage to Ishmael, going so far as to say that anyone claiming to be able to do so was a liar. This casts great doubt upon whether Muhammad was truly of the seed of Ishmael.
The next section comes from Ibn Sa‘d: .. he on the authority of Ibn ‘Abbas; he said: Verily the Prophet, WHENEVER he related his genealogy, DID NOT GO BEYOND MA‘ADD IBN ‘ADNAN IBN UDAD, then he kept quiet and said: The narrators of genealogy ARE LIARS, since Allah says: "There passed many generations between them."
Ibn ‘Abbas says: The Prophet would have been informed of the genealogy (prior to Adnan by Allah) if he (Prophet) had so wished.
.. he on the authority of ‘Abd Allah. Verily he recited "(The tribes of) ‘Ad and Thamud and those after them; NONE SAVETH ALLAH KNOWETH THEM." The genealogists ARE LIARS.
.. between Ma‘add and Isma‘il there were more than THIRTY GENERATIONS; but he did not give their names, nor described their genealogy, probably he did not mention it because he might have heard the Hadith of Abu Salih on the authority of Ibn ‘Abbas who narrated about the Prophet (may Allah bless them) THAT HE KEPT QUIET AFTER MENTIONING MA‘ADD IBN ‘ADNAN.
We begin with the statements of Ibn Kathir: There is no question of ‘Adnan being of the line of Ishmael, son of Abraham, upon both of whom be peace. What dispute there is relates to the number of forebears there were from ‘Adnan to Ishmael according to the various sources.
At one end of the spectrum, there is the extreme view that considers there to have been FORTY; this is the view of Christians and Jews who adopted it from the writings of Rakhiya, the clerk of Armiya (Jeremy) b. Halqiya, as we will relate.
Some authorities maintain there 30, others 20, yet more 15, 10, 9, or 7.
It has been said that the lowest estimate given is for FOUR, according to the account given by Musa b. Ya‘qub, on the authority of ‘Abd Allah b. Wahb b. Zum’a al-Zuma‘i from his aunt, and then from Umm Salama who stated that the Prophet (SAAS) said that the line was: "Ma‘ad b. ‘Adnan b. Adab b. Zand b. al-Tara b. A‘raq al-Thara".
Abu al-Qasim al-Suhayli and other Imams stated that the time lapse between ‘Adnan and Ishmael was too great for there to have been only 4, 10, or even 20 generations between them. That, they said, was because the age of Ma‘ad son of ‘Adnan was twelve at the time of Nebuchadnezzar.
Abu Ja‘far al-Tabari and others related that Almighty God sent a revelation at that time to Armiya’ b. Halqiya telling him to go to Nebuchadnezzar to inform him that God had given him rule over the Arabs. And God commanded to Armiya’ to carry Ma‘ad b. Adnan on the horse al-Buraq so that they would not bear him any rancour saying, "For I shall draw forth from his loins a noble Prophet by whom I shall seal the prophets."
‘Armiya did that, bearing Ma‘ad on al-Buraq to the land of Syria where he grew up among the Jews who remained there following the destruction of the temple at Jerusalem. There he married a woman named Ma‘ana, daughter of Jawshin unrest had quietened down and accord prevailed in the Arabian peninsula. Rakhiya, Armiya’s scribe, wrote his master's genealogy down in a document he had there which was to go into Armiya’s library; and he similarly preserved the genealogy of Ma‘ad.
And this is why Malik DID NOT ENTHUSE OVER THE ATTEMPT AT TRACING GENEALOGY BACK TO BEFORE ‘ADNAN.
As for Malik, God have mercy on him, he expressed disapproval when asked about someone tracing his descent back to Adam and commented: "WHENCE COMES TO HIM KNOWLEDGE OF THAT?" When he was asked about tracing back to Ishmael, he expressed similar disapproval, asking, "WHO COULD PROVIDE SUCH AN INFORMATION?" Malik also disliked tracing the genealogy of the prophets, such as saying, "Abraham son of so-and-so". Al-Mu‘ayti stated this in his book.
Al-Suhayli commented also that Malik's viewpoint was analogous to what was related of ‘Urwa b. al-Zubayr who is reported to have said, "WE HAVE FOUND NO ONE WHO KNOWS THE LINE BETWEEN ‘ADNAN AND ISHMAEL."
It is reported that Ibn ‘Abbas said, "Between ‘Adnan and Ishmael there were 30 ancestors WHO ARE UNKNOWN."
Ibn ‘Abbas is also reputed to have said when he traced back lines of descent as far as ‘Adnan: "The genealogists have LIED. TWICE OR THRICE." And that (scepticism) is even more characteristic of Ibn Mas‘ud, whose (attitude) was like that of Ibn ‘Abbas.
‘Umar b. al-Khattab stated, "We carry back the genealogy ONLY AS FAR AS ‘ADNAN."
Abu ‘Umar b. ‘Abd al-Barr stated in his book Al-Anba’ fi Ma‘rifat Qaba’il al-Ruwah that Ibn Lahi‘a related from Abu al-Aswad that he heard ‘Urwa b. al-Zubayr say, "WE NEVER FOUND ANYONE WHO KNEW GENEALOGY BACK PAST ‘ADNAN, NOR PAST QAHTAN, UNLESS THEY WERE USING CONJECTURE. "