The ruling was issued Wednesday by the New Orleans-based 5th U.S. Circuit Court of Appeals.
The ruling instructs a lower court to make changes that fix the "discriminatory effect" of the 2011 law in the months leading up to this fall's election.
But the ruling said the lower court should make changes that disrupt this year's election season as little as possible.
The Obama administration took the unusual step of deploying the weight of the U.S. Justice Department into the case when it challenged the law.