In a shock move, the 62-year-old said he had decided to step down after 11 years in Parliament over two spells.
He said: "After much soul-searching, I have decided not to stand in the 2017 General Election.
"At my age and after 11 years in Parliament, I have decided that it's time to step down and support a new Labour candidate for the city.
"As a proud Wulfrunian, it has been a privilege to serve the people of Wolverhampton as a Labour Member of Parliament. I look forward to campaigning hard for Labour in Wolverhampton."
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Apart from nine months in 2015 and 2016 as a shadow Treasury minister for Jeremy Corbyn, Mr Marris has spent his parliamentary career on the backbenches of the Commons.
His announcement came after Prime Minister Theresa May's call for a snap election on June 8 was backed by 522 MPs to 13 against in the House of Commons.
The Express & Star understands Paul Uppal, who narrowly lost Wolverhampton South West to Mr Marris in 2015, is the Tories' preferred choice to try and reclaim the seat from Labour.
Mr Uppal had previously ousted Mr Marris as MP in 2010, winning by 691.
Wolverhampton South West is one of the Tories' top targets because Mr Marris has a slender 801 vote majority.
Last night Mr Uppal was unavailable for comment but a senior Conservative Party source in the city said: "Paul, having successfully won the seat before and narrowly losing just two years ago, would be the favourite. Ultimately it is up to him."
Conservatives in the city are also thought to be considering Tettenhall Wightwick councillor Arun Photay if Mr Uppal decides against standing.
Labour Wolverhampton North East MP Emma Reynolds faces campaigning while on maternity leave.
She gave birth to a baby boy, Theo, on Good Friday. She is defending a 5,495-strong majority.
Wolverhampton South East Labour MP Pat McFadden has a 10,767 majority.