Dean has come in for criticism in the past week for dishing out two questionable red cards in the Premier League.
The 52-year-old sent off Southampton’s Jan Bednarek in the Saints 9-0 loss at Manchester United last Tuesday after consulting his pitch side monitor. The red card was later rescinded after Ralph Hasenhuttl’s side launched an appeal.
Dean was again in the news on Saturday at Craven Cottage when he dismissed West Ham United’s Tomas Soucek for what appeared to be an accidental elbow on Fulham striker Aleksandar Mitrovic. Soucek’s red card was also overturned on Monday following an appeal by the Hammers.
On the situation, Professional Game Match Officials Limited managing director, Mike Riley added: "Threats and abuse of this nature are totally unacceptable and we fully support Mike's decision to report these messages his family received to the police.
"Nobody should be victim of abhorrent messages like this. Online abuse is unacceptable in any walk of life and more needs to be done to tackle the problem."
Dean will be absent from this weekend’s Premier League action but will still take charge of the FA Cup fifth round game between Leicester City and Brighton and Hove Albion on Wednesday.