Foy sent off Willian and Ramires, as well as Chelsea manager Jose Mourinho, in Saturday's 1-0 loss at Aston Villa as the Premier League leaders' title challenge faltered.
Mourinho later called on the Premier League to stop sending Foy to officiate at Chelsea matches.
BBC Football Focus presenter Dan Walker on Saturday wrote on Twitter: "Poor old @chrishoy could be in for it tonight #FoynotHoy."
Hoy, who was at the Revolution Series event at the London Velodrome on Saturday night, responded: "They're coming thick and fast! With an emphasis on the 'thick'."
It is not the first time Hoy has been on the receiving end of abuse from football fans, with Chelsea supporters repeating their mistake, although some insisted the latest episode was a joke as Foy is not on Twitter.
Last April, in the days leading up to his official retirement announcement, Chelsea fans took to Twitter and targeted abuse at Hoy - intended for Foy - over his officiating in the previous weekend's FA Cup semi-final defeat to Manchester City at Wembley.
When Foy played a controversial role in Tottenham's loss to Stoke in December 2011 the abuse continued into a second day.
Hoy responded then: "Just for the record 1) I don't need glasses and 2)I do not lead a double life as an English premier league ref. That's Chris Foy.
"Still getting some rather amusing grief from Spurs fans! On the plus side I've learned some new 4 letter words today. #FoyNotHoy."