Is it permissible to offer a pregnant animal as an udhiyah?
Question

Is it permissible for us to offer a pregnant animal as an udhiyah? If that is permissible, then what should we do with the foetus?
Praise be to Allah.Firstly: 
The udhiyah is one of the rituals of Islam that is prescribed by the Book of Allah, may He be exalted, and the Sunnah of His Messenger (blessings and peace of Allah be upon him), and by the consensus of the Muslims. This has been discussed in fatwa no. 36432. 
For information on the conditions of the udhiyah, please see fatwa no. 36755. 
Secondly: 
The scholars differed as to whether it is permissible to offer a pregnant livestock animal as an udhiyah. The majority are of the view that it is permissible to offer it as an udhiyah, and they did not mention pregnancy among the faults or defects that render an animal unacceptable as an udhiyah. 
The Shaafa‘is differed from that, and were of the view that a pregnant animal should not be offered as an udhiyah. 
It says in al-Mawsoo‘ah al-Fiqhiyyah al-Kuwaitiyyah (16/281): 
The majority of fuqaha’ did not mention pregnancy as a defect with regard to the udhiyah, apart from the Shaafa‘is, who stated clearly that a pregnant animal is not acceptable as an udhiyah, because pregnancy affects the meat. End quote. 
It says in Haashiyat al-Bujayrami ‘ala al-Khateeb (4/335), which is a Shaafa‘i book: 
The pregnant animal is not acceptable, and this is the view of our madhhab, because pregnancy affects the meat. Rather it is regarded as acceptable in the case of zakaah, because what is sought in that case is the offspring, not the quality of the meat. End quote. 
The correct view is that a pregnant livestock animal is acceptable as an udhiyah, if there is no other defect in it. Shaykh Muhammad ibn Ibraaheem (may Allah have mercy on him) said: 
It is acceptable to sacrifice a pregnant sheep, if it is free of the defects mentioned in conjunction with sacrificial animals.
End quote from Fataawa wa Rasaa’il ash-Shaykh Muhammad ibn Ibraaheem (6/146) 
Thirdly: 
If the foetus is extracted alive, then it should be slaughtered in the prescribed manner and may be eaten. 
Ibn Qudaamah said in al-Mughni (9/321):
If it is extracted alive and in stable condition, and it could be slaughtered, but it is not slaughtered until it dies, then it is not regarded as having been slaughtered in the prescribed manner. Ahmad said: If it is extracted alive, then it must be slaughtered in the prescribed manner, because it is a separate soul. End quote. 
If it is extracted dead, then the majority of scholars are of the view that it may also be eaten, because it is as if it was slaughtered when its mother was slaughtered in the prescribed manner. 
Abu Dawood (2828), at-Tirmidhi (1476 – and he classed it as saheeh), Ibn Maajah (3199) and Ahmad (10950) narrated from Abu Sa‘eed that the Prophet (blessings and peace of Allah be upon him) said: “The foetus is slaughtered when its mother is slaughtered (in the prescribed manner).” Classed as saheeh by al-Albaani in Saheeh al-Jaami‘ (3431). 
This – as we have mentioned – is the view of the majority of scholars, with the exception of the Hanafis. 
Shaykh al-Islam Ibn Taymiyah said in Majmoo‘ al-Fataawa (26/307): 
Sacrificing a pregnant animal as an udhiyah is permissible. If the foetus is extracted dead, then its slaughter was the slaughter of its mother, according to ash-Shaafa‘i, Ahmad and others, regardless of whether it had any hair or not. If it was extracted alive, then it should be slaughtered. 
The view of Maalik is that is if it had hair, it is permissible, otherwise it is not. 
According Abu Haneefah, it is not permissible unless it is slaughtered in the prescribed manner after it is extracted. End quote. 
This issue has previously been discussed in detail, and we noted that some of the scholars regarded it preferable not to eat the foetus from a medical point of view. 
And Allah knows best.