A video had emerged of the cricketer doing an impression of the 15-year-old, who suffers with septo-optic dysplasia, after the youngster swore in response to a question during a TV appearance.
Harvey was asked by his mother during a live showing of ITV's Loose Women how he would response to online bullies, and he replied saying: "Hello, you cunt."
On Wednesday evening, the Durham all-rounder took to Twitter to apologise in a statement, which read: "Earlier this year I was a shown a clip of Harvey being asked on Loose Women how he responds to internet trolls. I loved Harvey's directness with his responses - he said what most of us think but perhaps aren't brave enough to say, let alone on live TV.
"I foolishly attempted to copy the clip after I saw it a few times. I should never have done this and I am so sorry. It was absolutely not my intention to offend Harvey, Katie or anybody else.
"I have written to both Harvey and Katie to say sorry and prior to this offered to meet in person at the end of last month with a view to also getting behind their petition about online bullying. I do hope I can put this right."
Stokes is currently suspended on full pay while police investigate an alleged assault outside a bar in Bristol last month.