Ibn Katheer (may Allah have mercy on him) said: 

It was narrated to us via Ibn Luhay‘ah from Qays ibn al-Hajjaaj from someone who told him: When Egypt was conquered, its people came to ‘Amr ibn al-‘Aas and said to him: O Ameer, this Nile of ours is used to something and cannot flow unless it is done. He said, What is that? They said: On the twelfth night of this month, we take a young girl from her parents, and we placate her parents, then we dress her in jewellery and the finest garments there can be, then we throw her into this Nile. 

‘Amr said to them: This is something that cannot happen in Islam; Islam erases that which came before it (of bad customs). 

So they stayed for a while, during which the Nile did not flow at all, neither a little nor a lot, until they thought of leaving. Then ‘Amr wrote to ‘Umar ibn al-Khattab, telling him about that. He wrote to him, saying: You did the right thing. I am sending you a piece of paper with my letter; throw it into the Nile. 

When his letter came, ‘Amr took the piece of paper on which was written: 

“From the slave of Allah ‘Umar, Ameer al-Mu’mineen, to the Nile of the people of Egypt.

To proceed: If you only flow on your own initative, then do not flow, for we have no need of you. But if you only flow on the command of Allah, the One, the Subduer, and He is the One Who causes you to flow, then we ask Allah, may He be exalted, to make you flow.” 

He threw the paper in the Nile and by Saturday morning, Allah had caused the Nile to flow (to a depth or width of) sixteen cubits in one night, and Allah put an end to that custom of the people of Egypt until today.

End quote from al-Bidaayah wa’n-Nihaayah, 7/114-115 

Similar reports were also narrated by Ibn ‘Abd al-Hakam in Futooh Misr, p. 165; al-Laalkaa’i in Sharh I‘tiqaad Ahl as-Sunnah, 6/463; Ibn ‘Asaakir in Tareekh Dimashq, 44/336; Abu’sh-Shaykh in al-‘Azamah, 4/1424, via Ibn Luhay‘ah. 

This is a da‘eef isnaad that is not saheeh, and this report cannot be proven with such an isnaad. Ibn Luhay‘ah – whose full name was ‘Abdullah ibn Luhay‘ah ibn ‘Uqbah – is da ‘eef as he used to get mixed up, and in addition to that he is mudallis. See at-Tahdheeb, 5/327-33; Mizaan al-I‘tidaal, 2/475-484 

Qays ibn al-Hajjaaj is sadooq, from the sixth level of hadeeth narrators (tabaqah) according to al-Haafiz Ibn Hajar; they are the ones who it is not proven that they met any of the Sahaabah. See: Taqreeb at-Tahdheeb, 1/25 

Sometimes he narrated it as a mursal report and sometimes he narrated it from the one who told him, but the one who told him is majhool and not known. 

So the report is da‘eef (weak) and is not saheeh (sound) 

If this story were true, everyone would know about it and it would be well known, and it would have been widely narrated through confirmed isnaads, because it is an important and significant event, the like of which should not be ignored; rather an incident less significant than this would not be overlooked by historians and narrators. 

And Allah knows best.