Suhailah died at the Damansara Specialist Centre at 12.30am. She was 82.
She leaves behind six children, one of whom is Defence Minister Datuk Seri Hishammuddin Tun Hussein.
Her other children are the late Datin Roquaiya Hanim, Puan Sri Dr Suraya Hani, Rodziah Hanis, Datin Dr Rozita Halina and Datuk Harris Onn.
Her remains will be taken to her family home at 19 Jalan Changkat Tunku, Bukit Tunku, Kuala Lumpur.
Members of the public can begin to pay their last respects from 9am today.
Prayers will be held at Masjid Negara at 12 noon before the funeral at the National Mausoleum.