It is narrated from Sayyiduna Bara’ bin ‘Azib (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) was asked:“From which animals should one avoid for sacrifice?”The Messenger of Allah (peace and blessings be upon him) indicated with his fingers and said,“One should avoid four.”Sayyiduna Bara’ bin ‘Azib (may Allah be pleased with him) would also indicate with his fingers and say,“My hand is smaller than the hand of the Messenger of Allah (peace and blessings be upon him).”(They are:) A lame animal that cannot walk, a one-eyed animal whose defect is obvious, a sick animal whose sickness is apparent, and an extremely thin animal that has no marrow.

It is narrated from Hazrat Nafi that Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) would avoid those sacrificial animals which were not musinnah and those which had any limb missing.
Imam Malik (may Allah have mercy on him) said: I like this narration very much.