The woman, identified as Asha Mehta, allegedly poisoned her one-year-old son Joy and four-year-old daughter Vantika before consuming it herself, they said.
Medical Officer Dr Irfan Vanjha has registered a complaint with Kalol (taluka) police in this regard.
Hospital authorities told police that Asha was in unconscious condition.
Police said they were getting details about Asha's family members.
"As of now none of her family members has come forward to inquire about her whereabouts," police said, adding they are investigating all angles in the case.