Mr Burt told MPs his decision had nothing to do with Brexit.
He informed David Cameron and Jeremy Hunt “a few weeks ago” that he would not be seeking a position in a reshuffled government.
He said he intends to continue his duties until September.
Raising a point of order at the end of health questions in the House of Commons, Mr Burt said: “Twenty-four years and one month ago I answered my first question as a junior minister in the House in oral questions and I have just completed my last oral questions.
A few weeks ago I made clear to the Secretary of State and to the Prime Minister and the Chief Whip that I wouldn’t after the referendum be seeking a post in what I expected to be a reshuffled government and in the event I hope to carry on with my duties until September, but there won’t be another oral questions.”