The deceased was identified as Khadijatul Kubra and the injured were Sajib Ahmed,6, and Ayesha Sultana,3.
Family members said Khadija found the cocktail in the nearby playground at Shontoner Mor mistaking it for a ball and brought it home.
When she was playing with Sajib and Ayesha with the ball the device exploded, injuring all of them.
Khadija died on the way to a hospital in Dhaka.
The injured victims were admitted to Jashore General Hospital.
Kotwali Police Station Officer-in-Charge Abul Hasnat said police visited the scene and are investigating the matter, reports UNB.