It is believed that Madam Ding Weibo fractured her skull after hitting her head on a seat.
The bus driver had apparently applied the brakes suddenly.
Madam Ding and her daughter had just boarded bus service No. 167 at about 8pm at Orchard Road, near Heeren shopping centre, when the driver jammed the brakes.
Both made a grab for the handrails, but the force of the brake threw Madam Ding onto the floor.
She was sent unconscious to the Singapore General Hospital.
Her daughter, Ding Xiao Sui, told Channel NewsAsia that Madam Ding suffered internal bleeding, and had to have an operation.
She is still in critical condition.
The family plans to lodge a complaint against the driver.
Her daughter said: "I was so scared and panicked, I did not know what to do. I kept calling for her, but there was no response. She was fine in the afternoon, she was shopping, and now she is in this state."
In a statement, SMRT said: "We are sorry the incident happened and investigations are on-going. We will be in touch with the family..."
Woman in coma after falling onboard SMRT bus - Channel NewsAsia