In The Name of Allaah, The Most Merciful, The Bestower of Mercy.
The Messenger [sallal laahu alayhi Wasallam] said, “Eat olive oil and anoint yourselves with it, for indeed it is from a blessed tree”.
Shaikh Zaid Bin Haadi [rahimahullaah] said, “This is something permissible. There is great benefit in olive oil and from that is what the Prophet [sallal laahu alayhi Wasallam] has stated, “Eat and anoint yourselves with it”, and he mentioned the reason that it is a blessed tree. And it suffices that Allaah [The Mighty and Majestic] made an oath by it in the Qur’aan, saying: [وَٱلتِّينِ وَٱلزَّيۡتُونِ – By the fig, and the olive]. [Surah At-teen. Aayah 1] And Allaah also praised it a second time in Surah Al-Muminoon when He said: [وَشَجَرَةً۬ تَخۡرُجُ مِن طُورِ سَيۡنَآءَ تَنۢبُتُ بِٱلدُّهۡنِ وَصِبۡغٍ۬ لِّلۡأَڪِلِينَ – And a tree (olive) that springs forth from Mount Sinai, that grows oil, and (it is a) relish for the eaters]. [Surah Al-Muminoon. Aayah 20] [An Excerpt from At-taleeqaat Al-Maleehah Alaa Silsilah Al-Ahaadeeth As-Saheehah. Page Vol1. Page 377. Slightly paraphrased]