Vardy's fiancée responded to one user by writing: "There are no words for people like you! You need locking up." She also wrote to another: "You sick f****** t***."
The tweets, which included sexual threats being sent about Sofia, are too graphic to publish in full.
The accounts, which were run by Twitter users claiming to be Manchester United supporters, are no longer active.
Fans were left angry by the abuse and sent support to Vardy. One wrote: "Disgusting and sick."
Another added: "Just to point out, not all Manchester United fans are like this. I'm sorry if those idiots have offended you."
A statement from Leicestershire Police said: "We are aware of the tweets and are currently liaising with the club. No formal compliant has yet been made."
A Leicester City spokesman 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.'
Leicester's win over Southampton on Sunday moved them seven points clear at the top of the Barclays Premier League with only six games to go until the end of the season.
- Daily Mail