The Swansea City defender was one of the front runners for the job as Wales prepare to play England at the Millennium Stadium on Saturday.
However, Wales boss Gary Speed has elected to go for Arsenal midfielder Ramsey who has just returned to action following a long lay off with a broken leg.
Speed told BBC Sport "I thought about it a lot
"As I have mentioned before, it is about the future and planning ahead.
"There were two or three candidates. I thought about what is best for the team going forward.
"I spoke to Aaron before making the decision and told him there were certain responsibilities and duties that would go with it, and to see if he was happy with it.
"I'm delighted and he was really happy. I made the decision because I thought it was best for the team and the future of the team."
Neil Taylor and Joe Allen are both in the squad alongside Williams.