The graphic abuse came after the Leicester player's fiancee posted pictures of the toddler wearing a Foxes shirt ahead of their match against Southampton on Sunday.
Leicestershire Police has launched an investigation into the shocking threats after a formal complaint was made on Monday.
Rebekah Nicholson tweeted the shots of her daughter wearing the blue T-shirt with 'Daddy' emblazoned on the back, which prompted rape threats on the social networking site.
She responded to one: "There are no words for people like you! You need locking up," while Vardy posted a screenshot of the threats, with the words "shocking and vile".
Leicestershire Police said: "Leicestershire Police is investigating a report of malicious communication being sent via social media.
"A report was made (on Monday) of an abusive message being received (on Sunday evening) by a woman on Twitter
Inquiries remain ongoing and the force is liaising with Leicester City Football Club."
Leicester called the abuse "shocking"
A spokesman for the Barclays Premier League leaders said: "We have offered our full support to Jamie and his family in dealing with this shocking abuse and referred the matter to the police."
Source : PA
Source: PA