In a statement issued to Deadline by Smith and director Antoine Fuqua, the pair said they felt "compelled" to act.
"We cannot in good conscience provide economic support to a government that enacts regressive voting laws that are designed to restrict voter access."
Some feel the new law will restrict voting by disadvantaged groups.
Will more film companies pull out?
Deadline said the move by the Emancipation producers comes after weeks of discussions between the filmmakers, film officials and Georgia political leaders, including voting rights activist Stacey Abrams.
It is the first film to pull out of the state since the new laws came into effect - but others could follow suit.
Director James Mangold, who will helm the new Indiana Jones movie, recently said he would not make any new movies in Georgia because of the new law.
"Georgia has been using cash to steal movie jobs from other states that allow people to vote," he tweeted. "I don't want to play there".
Star Wars actor Mark Hamill endorsed Mangold's tweet with hashtag #NoMoreFilminginGeorgia.
According to Georgia's film commission, more top-grossing movies are shot there "than anywhere else in the world" - with recent productions including Deadpool, Avengers: Endgame, Wandavision, Stranger Things and The Walking Dead.
Film and TV production now generates more than $10bn (£7,2bn) for the state each year - and Abrams, who opposes the new laws, has urged Hollywood not to move away en masse.
Martin Luther King Jr's daughter, Bernice King, has also asked film-makers to reconsider. "Please stop the #BoycottGeorgia talk," she said. "That would hurt middle class workers and people grappling with poverty. And it would increase the harm of both racism and classism."
What do the new laws say?
In future elections, ID will be required for anyone requesting a mail-in ballot.
Proponents of the bill say this method will make postal voting more secure, but critics argue the new measures are likely to disproportionately affect black Americans, who are less likely than white Americans to have voter identification
The law also prohibits anyone except poll workers from handing out food or water to people queuing outside polling stations - and there will be a limit on the number of "drop boxes" in which people can place their absentee votes, meaning many will have to travel further.
The early voting period for all run-off elections - in Georgia, no candidate can advance through a primary or a general election system without first earning more than 50 percent of the votes - will also be shortened.
President Joe Biden has described the move as an "atrocity", saying it disproportionately targeted black Americans.