In a letter to constituents, the Oxford East MP wrote: "This election is for a Parliament which is likely to run until 2022, when I would be over 71."
By the time of the general election on 8 June, the 66 year old will have held his seat for 30 years.
He is the county's only Labour MP and served in Tony Blair's government as chief secretary to the treasury.
In a letter to his constituents, he added: "My belief and confidence in the values of fairness which Labour stands for are as strong as ever, and I will work tirelessly to help secure the election of a Labour MP for Oxford East."
In the 2015 general election, Mr Smith increased his majority despite suspending his campaigning following death of his wife Val, the former Lord Mayor of Oxford.
Analysis: Bethan Phillips, BBC Oxford political correspondent
Andrew Smith's decision not to stand as a candidate does mean that Oxfordshire will get at least one new MP this summer.
And other parties will now be looking at the Oxford East constituency with interest.
It's seen as a safe Labour seat - Andrew Smith got a majority of more than 15,000 at the last election, with the Conservatives getting a surprise second place.
But look back to 2005 and the Liberal Democrats came within 963 votes of winning.
The former work and pensions secretary came under criticism by some Labour supporters in 2015 when he provided the 35th vote required for Jeremy Corbyn to be on the ballot in the party's leadership election.
Mr Smith, who actually supported Yvette Cooper, said it would have been "indefensible" to leave Mr Corbyn off the ballot paper.
But he later echoed calls from colleagues for his party's leader to resign.
In 2016, he said: "We cannot go into a general election with a leader with such lack of support from MPs and a significant section of the wider membership."
The Oxford Labour Party said the National Executive Committee will begin selection procedures for its prospective candidate.
Oxfordshire's longest-serving MP, Andrew Smith, has announced he will not stand in June's snap election.