"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," England international Keane told the club's website http://www.evertonfc.com/news/2018/08/26/keane-injury-update.
Everton said Keane did not suffer any other complications.
"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."
Keane had earlier scored Everton's second goal of the match after Theo Walcott's opener. Bournemouth, however, fought back with second-half goals from Josh King and Nathan Ake to earn a point at the Vitality Stadium.
"I was so happy to get my first Premier League goal for Everton," Keane said. "I'm just gutted we didn't take the three points, but we keep our unbeaten start going."
Everton have two draws and a win from their three matches and host Huddersfield Town next weekend.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
