Capello has offered the injured midfielder a place in the travelling party to South Africa.
And said in his column for The Sun, Wright said: "David, please accept Fabio Capello's offer to still join England at the World Cup.
"Believe me, if you don't, you could regret it for the rest of your life.
"I know from personal experience the nightmare you are going through right now, and how much playing for England means to you.
"If ever there's a footballer who embodies what playing for England is meant to be about, it's you.
"I felt sick to the core when I saw you suddenly pull up playing for AC Milan on Sunday. I knew straight away you were in trouble and that this was a serious injury.
"Like everyone else I was clinging to the hope there could be a miracle cure - although deep down I suspected that wouldn't be the case.
"Now I'm just gutted you won't be able to make it to South Africa."