Tengku Sulaiman Shah was born on 1 Ramadhan 1369 Hijrah (the first day of the holy Islamic month of Ramadan), corresponding to 17 June 1950 of the Gregorian calendar at the Istana Raja Muda Selangor in Kampung Baru, Kuala Lumpur which was the then-state capital of Selangor at that time.

He is the fourth child and second son of the then-Raja Muda (Crown Prince) of Selangor, Tengku Abdul Aziz Shah (1926–2001) and his first wife, YMM Raja Saidatul Ihsan binti Almarhum Tengku Badar Shah (Paduka Bonda Raja Selangor) (1923–2011).

On 15 January 1972, his father, the then-Sultan of Selangor, Sultan Salahuddin Abdul Aziz Shah Al-Haj appointed Tengku Sulaiman Shah Al-Haj as the Tengku Panglima Besar and held the post for six years.

On 1 July 2016, his elder brother, the incumbent Sultan of Selangor, Sultan Sharafuddin Idris Shah Al-Haj, promoted Tengku Sulaiman Shah Al-Haj to Tengku Laksamana of Selangor.

He was attached in Audio Visual department and gained wide knowledge in the advertising and branding industry.

Tengku Sulaiman Shah Al-Haj's interests includes photography and travelling.

Their youngest son, Tengku Shariffuddin Shah, married celebrity Juliana Evans in 2017.