A prostration when reciting Sad is not one of those which are divinely commanded, but I have seen Messenger of Allah (ﷺ) prostrate himself.
Sunan Abi Dawud Book 7, Hadith 9
← Previous Hadith I offered the night prayer behind Abu Hurairah. He recited Surah Inshiqaq ("When the sky is rent asunder") and prostrated himself. I asked him: What is this prostration ? He replied: I prostrated myself on account of this (surah) behind Abu al-Qasim (i.e. the Prophet). I shall continue prostrating on account of this till I meet him.

Sunan Abi Dawud Book 7, Hadith 8 Next Hadith → The Messenger of Allah (ﷺ) recited surah Sad on the pulpit. When he reached the place of prostration (in the surah), he descended and prostrated himself and the people prostrated with him. When the next day came, he recited it. When he reached the place of prostration (in the surah), the people became ready for prostration. Thereupon the Messenger of Allah (ﷺ) said: This is the repentance of a Prophet ; but I saw you being ready for prostration. So he descended and prostrated himself and the people prostrated along with him.

Sunan Abi Dawud Book 7, Hadith 10