The state government has been asked to reply within four weeks.
Sharma, a BJP Yuva Morcha leader, was arrested on May 10 on a complaint by a local Trinamool Congress (TMC) leader and charged with defamation under Section 500 of the Indian Penal Code and under provisions of the Information Technology Act.
The top court has termed her arrest as "prima facie arbitrary" and granted her bail ordering "immediate release".
However, a petition filed by her brother Rajiv Sharma in the Supreme Court alleged that there was a deliberate delay in releasing Sharma and that she was kept in jail for an extra day.
A bench headed by Chief Justice Ranjan Gogoi took exception to the delay by the West Bengal government in keeping Sharma behind the bars despite the bail order.
The state government said her release took time due to delay in receiving a certified copy of the top court order, which is mandatory as per the state's jail manual rules.
"This is not done. First of all, her arrest was arbitrary... And jail manuals can't have superintendence over the Supreme Court," said the apex court.
Sharma was accused of sharing on the social media a photo of Banerjee photoshopped on a picture of Bollywood actor Priyanka Chopra from a MET Gala event held in New York City.
( With inputs from IANS )