The graphic abuse came after the Leicester striker's fiancee posted pictures of the toddler wearing a Foxes shirt ahead of their match against Southampton on Monday.
Rebekah Nicholson tweeted the shots of her daughter wearing the blue T-shirt with "Daddy" emblazoned on the back, which prompted shocking rape threats on the social networking site.
She responded to one: "There are no words for people like you! You need locking up."
Vardy posted a screenshot of the threats, with the words "shocking and vile".
Fans took to twitter to express their dismay at the tweets towards the England striker's daughter.
Police are in contact with Vardy's club Leicester over the abuse.
A spokeswoman for Leicestershire Police said: "We are aware of the tweets and are liaising with the club. No formal complaint has yet been made."
She added that if a complaint is made, the force will launch an investigation.