Her father, Tengku Seri Setia Raja Terengganu Tengku Hitam Omar, was a member of the Singapore (Johor Bendahara Horeh) royal family, serving in the Terengganu State Civil Service as the State Secretary of Terengganu; he was exiled since the death of the last Sultan of Singapore, Alauddin Alam Shah, in 1897.

Tengku Intan received her education at the Malay School in Telok Kurau and Katong Convent, Singapore.

Tengku Intan married Sultan Ismail Nasiruddin Shah ibni Almarhum Sultan Zainal Abidin III (then Tengku Paduka Raja of Terengganu) on 3 April 1944 as his second wife.

In 1979, upon her husband's death she was created Tengku Ampuan (Queen Dowager) of Terengganu.

In 1998, on the death of her stepson, Sultan Mahmud Al-Muktafi Billah Shah, she became Tengku Ampuan Tua (Grand Queen Dowager) of Terengganu.