The fuqaha’ differed concerning this issue and there are two views:
The first view is that the udhiyah may also count as ‘aqeeqah. This is the view of al-Hasan al-Basri, Muhammad ibn Sireen and Qataadah, and it is the view of the Hanafis, and one of two views narrated from Imam Ahmad.
They regarded this issue as being like when Jumu’ah and Eid fall on the same day, and offering one of the two prayers counts for the other one too, because they have in common the number of rak’ahs, the khutbah and the fact that Qur’aan is recited out loud in the prayer, so the actions are the same. The same applies here, the act of slaughtering the animal is the same.
They also said: It is like when the Muslim prays two rak’ahs intending them to be both greeting the mosque and the regular Sunnah.
The second view is that the udhiyah does not count as the ‘aqeeqah too. This is the view of the Maalikis and Shaafa’is, and it is the other view narrated from Imam Ahmad.
These scholars said that the udhiyah and ‘aqeeqah are two different sacrifices offered for different reasons, so one of them cannot count as the other one too, just as if the sacrifice offered by the pilgrim doing tamattu’ and the sacrifice offered as a fidyah are combined, the one cannot count as the other too.
And they also said that the point of offering udhiyah and ‘aqeeqah is to shed the blood of the animal in both cases, because they are two rituals with the aim of shedding the blood of the animal, therefore one cannot count as the other too.
Ibn Hajar al-Makki al-Shaafa’i was asked about slaughtering a sheep on the days of sacrifice with the intention of both offering a sacrifice and offering ‘aqeeqah: does it serve both purposes or not?
What is indicated by the words of our companions and we have been holding this view for many years, is that they cannot be combined, because both the udhiyah and the aqeeqah are Sunnah and each is done for its own sake and is done for a reason that is different than the other. The purpose behind one is not the same as the purpose behind the other, because the udhiyah is a sacrifice offered on behalf of oneself and the ‘aqeeqah is a sacrifice offered on behalf of one's child, because by its blessing one hopes that the child will be righteous and kind to his parents and may intercede for them. Saying that they may be combined negates the purpose behind both of them, so we cannot say that. This is like what they say about the Sunnah of doing ghusl for Jumu’ah and doing ghusl for Eid, and the Sunnah prayers of Zuhr and ‘Asr. As for the prayer to greet the mosque and so on, they are not done for their own sake, rather that is done so as not to transgress against the sanctity of the mosque, and that may be achieved by offering any other prayer. The same applies to fasting Mondays, because the purpose is to fill this day with worship by observing this special fast, but it may be achieved by observing any other fast on that day. But this does not apply to udhiyah and ‘aqeeqah, so they are not like that, as is clear from what I have stated… End quote.
Al-Fataawa al-Fiqhiyyah (4/256).
What seems to be the case – and Allaah knows best – is that it is acceptable to offer one sacrifice with the intention of ‘aqeeqah and udhiyah. This view was favoured by Shaykh Muhammad ibn Ibraaheem (may Allaah have mercy on him). We have mentioned his view and those of others in the answer to question no. 106630.
And Allaah knows best.