The Welsh region says Smith, 28, has suffered a "series of concussive events" and after "expert advice" has decided to "hang up his boots".
"I am utterly disappointed and devastated that I have been forced to retire through injury," said Smith.
"But I feel that the medical advice given to me cannot be ignored."
Former Wales Under-20 captain Smith, made more than 160 appearances for Dragons since joining the Rodney Parade side in 2005.
Dragons' director of rugby, Lyn Jones said it was a "big blow" for the region.
"We are all so upset at the news of Ashley's forced retirement," said Davies.
"Over his 10 years at Rodney Parade, he has been a credit to the region, himself and his family.
"We will miss his maturity, football, decision making and his experience.
"It's a big blow for us, but Ashley has made the right decision for himself and his family. We wish him well for the future."
Newport Gwent Dragons centre Ashley Smith has retired from playing rugby on medical grounds.