Special CBI judge OP Saini issued a notice to CBI and sought its reply by Tuesday on the application.
The application said her medical records indicate she is suffering from Alzheimer's disease and is undergoing treatment for the past one year.
"Taking into consideration her mental and physical condition, the court may be pleased to exempt her from appearing and dispense with her presence," the plea said.
It also said if the court feels, it can constitute a medical board to examine Dayalu Ammal and give its report on her condition.
In its second chargesheet filed on April 25, 2011, the CBI had named Dayalu Ammal as a prosecution witness in the case in which DMK MP and M Karunanidhi's daughter Kanimozhi is facing trial along with others, including former telecom minister A Raja.