The announcement, which appeared to take even his own party by surprise, means the election will become an effective referendum on the controversial 42-days detention issue.
Conservative leader David Cameron called Davis' decision courageous and brave but stopped short of backing it. The government said it proved the Tories are in disarray.
Davis was a leading critic of the plan to increase the possible pre-charge detention time for terrorist suspects to 42 from 28 days, on which the government narrowly won a Commons vote late on Wednesday.
Davis, 59, said he was "taking a stand".
"I will argue in this by-election against the slow strangulation of fundamental British freedoms by this government," he told reporters outside parliament.
"Now that may mean I have made my last speech to the House ... and of course that would be a cause of deep regret to me.
"But at least my electorate and the nation as a whole, would have had the opportunity to debate and consider one of the most fundamental issues of our day -- the ever intrusive power of the state on our lives, the loss of privacy, the loss of freedom and a steady attrition undermining the rule of law."
He said if his electorate voted him back into parliament, "it will be with a single, simple message -- that the monstrosity of a law that we passed yesterday will not stand".
Cameron said the decision was a personal one that had not been taken after consultation with senior Tory officials.
"David Davis has made a very courageous (and) a very brave decision," he told reporters in Cornwall. "I wish him well in his by-election campaign.
Later in several media interviews, Davis denied speculation that his decision had caused a rift with Cameron, the man who beat him in the 2005 Conservative leadership election.
The Liberal Democrats, who also oppose the 42-day plan, said they would not fight the by-election in Davis' east Yorkshire constituency of Haltemprice and Howden which he held with a majority of 5,116 in 2005.
That decision means it will be a straight fight between Labour and the Conservatives and keep the controversial issue of pre-charge detention in the spotlight, to the discomfort of Prime Minister Gordon Brown.
Commentators have said Brown, his popularity at record lows in opinion polls, had used up substantial "political capital" to win Wednesday night's vote.
Davis will be replaced on the Tory front bench by the current Shadow Attorney General Dominic Grieve.
Home Secretary Jacqui Smith said the decision proved the opposition was in disarray.
"Faced with a crucial decision on the safety and protection of the British public, the Conservatives have collapsed into total disarray on what is their first big policy test since they have come under greater scrutiny," she said in a statement.
"David Cameron must come clean on what has really happened and why David Davis has really resigned."
