Praise be to Allah.
What is sujud al-shukr?
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
“Sujud al-shukr is done in response to a calamity that is averted or a blessing which comes to a person. It is like sujud al-tilawah outside prayer. Some of the scholars said that wudu and takbir is required, and some said that only the first takbir is required. Then he should fall down in prostration, and make du`a after saying “Subhana Rabbiy al-A’la (Glory be to my Lord Most High).” (Fatawa Islamiyyah, 1/205)
What du`a should you say in sujud al-shukr?
There is no specific du`a narrated in the hadiths for sujud al-shukr. Hence the scholars said that what is to be said in sujud al-shukr is the same tasbih and du`a as are said when prostrating in prayer.
So one should say “Subhana Rabbiy al-A’la. Allahumma laka sajadtu wa bika amantu wa laka aslamtu, sajada wajhi lilladhi khalaqahu wa sawwarahu wa shaqqa sam’ahu wa basarahu, tabaraka Allah ahsan ul-khaliqin (Glory be to my Lord Most High, O Allah, unto You I prostrate, in You I believe and to You I submit. My face has prostrated to the One Who created and formed it, and gave it hearing and sight. Blessed be Allah, the best of creators). Then he should make du`a as he likes.
Ibn Qudamah (may Allah have mercy on him) said:
“The description, rulings and conditions of sujud al-shukr are the same as those for sujud al-tilawah (prostration required when reciting certain verses of Quran).” (Al-Mughni, 2/372)
And he said concerning sujud al-tilawah: “One should say in this prostration what he says in the prostration during prayer.” (Al-Mughni, 2/362)
And Allah knows best.