Do durational residency requirements violate the Equal Protection Clause of the Fourteenth Amendment?

 According to the U.S. Supreme Court in Dunn v Blumstein, yes.

- What is a durational residency requirement? 

It includes an acknowledgement of a right to interstate travel.

From Oyez: 

Facts of the case: 

A Tennessee law required a one-year residence in the state and a three-month residence in the county as a precondition for voting. James Blumstein, a university professor who had recently moved to Tennessee, challenged the law by filing suit against Governor Winfield Dunn and other local officials in federal district court.

Question: 

Did Tennessee's durational residency requirements violate the Equal Protection Clause of the Fourteenth Amendment?

Conclusion: 

In a 6-to-1 decision, the Court held that the law was an unconstitutional infringement upon the right to vote and the right to travel. Applying a strict equal protection test, the Court found that the law did not necessarily promote a compelling state interest. Justice Marshall argued in the majority opinion that the durational residency requirements were neither the least restrictive means available to prevent electoral fraud nor an appropriate method of guaranteeing the existence of "knowledgeable voters" within the state.