Hishammuddin Hussein, a cousin of Najib's, said 83-year-old Sri Siti Amirah was "on the flight". Siti Amirah was also Hishammuddin's step-grandmother.
"Pls pray 4 her," he wrote on his Twitter feed above a photo of her in an Islamic headscarf.
The defence minister's tweet confirmed an earlier report in the Star newspaper that said Siti Amirah had embarked alone in Amsterdam on board flight MH17 en route to the Indonesian city of Jogjakarta.
She was scheduled to transit at Kuala Lumpur International Airport.
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Siti Amirah, a native of Indonesia, was headed there to celebrate Eid al-Fitr, Islam's biggest festival, at the end of the Muslim holy month of Ramadan, the Star report quoted a family spokeswoman as saying.
Both Malaysia and Indonesia are Muslim-majority countries.
"She was a very, very nice lady. A kind-hearted, beautiful woman. She was a homemaker who looked after my grandfather very well. We called her 'ibu' (mother)," the family spokeswoman told the newspaper.
Najib, 60, is the son of Malaysia's second prime minister Abdul Razak, while Hishammuddin is the son of the country's third premier Hussein Onn.
The mothers of Hishammuddin and Najib are siblings.