Since colliding with a scrum machine on October 26, the 2003 World Cup winner has experienced dizziness and numbness, and will undergo neck surgery again tomorrow.
"I went to the specialist and he advised me it isn't safe to carry on playing," said Thompson, who sustained the injury only two days before making his debut for his new side after joining from Leeds on a three-year deal.
"I can't do what I need to do to earn a living. I scrum - that is what I do. I tried to convince myself it was fine and it wasn't. I have got to accept it this time. There is no way I can play.
"I was gutted. I hit a scrum machine and it just went. I played 60 minutes at Worcester and that was it. I tried to convince myself it was fine and it wasn't.
"I need another operation, which will happen on Tuesday. I have had a lot of numbness and dizziness."
Thompson lasted an hour in Wasps' 14-12 victory at Worcester in October, which proved to be the last professional rugby match for the hooker who was capped 73 times by his country and made three British and Irish Lions appearances.
He returned a £500,000 insurance payout when he made a comeback after his last neck injury, after receiving a second medical opinion that cleared him to play again.
He added: "I was enjoying rugby. I thought I had done all right at the World Cup. To finish the way it did was really disappointing and then to suffer another blow a few weeks afterwards - it is like a kick in the nuts.
"This operation will be more painful than the last one. I will take a break and see what opportunities come along the way.
"I was really looking forward to Wasps. Dai Young is someone I really wanted to play for."
Young, the Wasps director of rugby, said: "We have huge sympathy with Steve who we know was really looking forward to becoming an integral part of Wasps.
"He is leaving behind a superb legacy in the game with some massive achievements and we wish him all the best in the future."
Damian Hopley, chief executive of the Rugby Players' Association, said it was a huge loss to English rugby that one of the great personalities of the game over the past decade had to call it a day.
He said: "It is a huge blow that he has had to retire prematurely, especially after the incredible amount of hard work and character he showed in coming back from a seeming career-ending injury to play at the highest level.
"Given Steve's popularity, humility and determination, I have no doubt that he will go on to be extremely successful, be that in or out of rugby.
"On behalf of all the RPA members, I would like to wish Steve every success for the next exciting chapter of his life."