The 25-year-old sustained a small hairline fracture of the skull in the game against Bournemouth at the Vitality Stadium.
Keane will not be back in training before next month as he will be unable to engage in head contact for between three and four weeks.
Keane told the club’s official website: “Thank you to everyone for all the well wishes and support.
“I’m okay but suffered a small hairline fracture of the skull which will heal itself and means I won’t be able to have any head contact for three to four weeks.
“I will be back with my team and back on the pitch as soon as I can after that.
“I also want to say a huge thank you to the medical staff at Everton and Bournemouth as well as all those at Poole Hospital for their excellent treatment and care.”