Jesus put a stop to this practice and thats where Islam picked up from… Stoning has nothing to do with Christianity or Islam. Please read below.
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The Christian answer to this question is found in the amazing and touching story narrated by the Apostle John. One day when Jesus Christ was teaching in the Temple, "the doctors of Law (Rabbis) and Pharisees brought in a woman caught committing adultery. Making her stand out in the middle they said to him, ‘Master, this woman was caught in the very act of adultery. In the Law Moses has laid down that such women are to be stoned. What do you say about it?’…
"Jesus bent down and wrote with his finger on the ground. When they continued to press their question he sat up straight and said, ‘That one of you who is faultless shall throw the first stone.’ Then once again he bent down and wrote on the ground. When they heard what he said, one by one they went away, the eldest first; and Jesus was left alone, with the woman still standing there. Jesus again sat up and said to the woman, 'Where are they? Has no one condemned you? She answered, ‘No, one sir.’ Jesus said, ‘Nor do I condemn you. You may go; do not sin again’ " (John 8:1-11).
The holy Quran does not prescribe stoning as the punishment for adultery. There is not a single verse to this effect. The Holy Quran stipulates the punishment of “a hundred stripes” for the act of adultery, zina (24:2). If a particular sentence is prescribed in the Holy Quran a harsher one cannot be imposed. The holy Quran also requires the fulfilment of an almost impossible condition before conviction can result. Four eye- witnesses have to testify to sustain the charge (24:4).
And if those who accuse a woman and fail to “produce four witnesses”, they are then to be flogged eighty times. If there are no witnesses and a husband accuses his wife of adultery he has to repeat his testimony and on the fifth invoke the “Curse of Allah” on himself if he is lying (24:6-7). The punishment is averted if the wife similarly swears (24:8-9). Therefore, the Holy Quran here places greater reliance on the testimony of a woman.
In none of the verses pertaining to adultery in the holy Quran the term stoning (rajama / rajim) is used. ‘Rajim’ means ‘stoned’, ‘accursed’ or ‘damned’ and is used as an epithet of Satan (3:36, 15:17, 16:98 Shaitan nir rajim, Satan the stoned or accursed). The verb which derives from rajim is rajama, and it means ‘to stone’, ‘the act of stoning’, ‘a missile’, ‘something to stone with’, ‘guesswork’, ‘guessing’ or ‘stoned’ (11:91, 18:20, 19:46, 36:18, 44:20, 18:22, 67:5 and 26:116). However, none of the verses refer to adultery. The Arabic word rajim / rajama is similar to the Hebrew word ragam, which means ‘to collect or cast stones’.
How is it then that some Muslims followed the Jewish practice and prescribed stoning as the punishment for the sin of adultery? **