Vietnam had been pushing for her release, and the decision comes days after her Indonesian co-defendant, Siti Aisyah, was unexpectedly freed.
Both women insist they are innocent.
Kim Jong-nam was assassinated with liquid VX nerve agent at Kuala Lumpur airport in February 2017.
Ms Huong says she was tricked into taking part and believed she was part of a TV prank.
The 30-year-old, who could face the death penalty if convicted, sobbed in court when it was announced that her trial would go ahead.
She told reporters: “Only God knows that we did not commit the murder. I want my family to pray for me,” AFP news agency reports.
Her lawyer said she had been unable to sleep since the unexpected release of Siti Aisyah, who flew to Jakarta the day she walked free from court.
Ms Huong, who arrived at court in a bulletproof vest and red headscarf, has already been on trial for a year and a half.
The presiding judge ruled that the case would continue, but adjourned it until 1 April as the defendant was not “physically and mentally” well enough to continue with the proceedings.
Vietnam’s government said it was disappointed by the outcome of the hearing.
“We regret the fact that the Malaysian court did not set free Doan Thi Huong immediately,” a foreign ministry spokeswoman said.
Earlier Vietnamese Foreign Minister Pham Binh Minh asked Malaysia to “ensure a fair trial for Huong and set her free”. Vietnam’s justice minister had also written to Malaysia’s attorney-general asking for her release.
How did the murder happen?
Kim Jong-nam, the estranged half-brother of North Korea’s leader Kim Jong-un, had been waiting to board a flight from Kuala Lumpur to Macau on 13 February 2017 when two women approached him in the departure area.
CCTV footage showed one of them placing her hands over his face, then both women leaving the scene.
Mr Kim died on the way to hospital from what was later found to be exposure to the nerve agent VX, one of the most toxic of all known chemical agents.
North Korea has fiercely denied any involvement in the killing, but four men – believed to be North Koreans who fled Malaysia on the day of the murder – have also been charged in the case.
They remain at large despite an Interpol “red notice”, equivalent to an international arrest warrant.
Who was Kim Jong-nam?
Kim Jong-nam was the older half-brother of North Korea’s authoritarian ruler, Kim Jong-un.
He was once seen as a future leader of the isolated country, but when his father Kim Jong-il died, he was bypassed in favour of the younger Kim.
He was largely estranged from the family, and spent most of his time overseas in Macau, mainland China and Singapore.
He had spoken out in the past against his family’s dynastic control of North Korea, and in a 2012 book was quoted as saying he believed his half-brother lacked leadership qualities.