Two children who go to the Miles of Smiles nursery in Baglan have been confirmed as having the virus, while five others are being tested.
A vaccination session is planned at the nursery on Friday for children who have not had the MMR.
Parents who cannot attend should make an appointment with their GP.
Public Health Wales (PHW) said vaccination uptake at the nursery was good but some children were at risk because they were too young to have received one or both doses of the vaccine.
Last July saw the end of Wales' biggest outbreak of the infection in Swansea, which resulted in 1,200 reported cases and one death.
Dr JÃ¶rg Hoffmann, of PHW, said: "While two cases of measles may not sound a lot, we have five other children with symptoms, all attending a nursery school where there are children who are too young to be fully-vaccinated and could easily catch and spread measles."
He said parents in the wider Neath area should also get their children vaccinated.
Symptoms of measles include a fever, tiredness, runny nose, conjunctivitis and a distinctive red rash.
It is very contagious, can cause serious complications and in rare cases can be fatal.

Originally built by Henry VIII to defend the coast from invasion, Hurst Castle was also used to guard the Solent during World War Two.
The £1m conservation project will repair parts of the castle added in the 20th Century.
English Heritage said it would ensure the site was "protected for the future".
Hurst Castle was originally built by Henry VIII between 1541 and 1544 to guard the Needles Passage, the narrow western entrance between the Isle of Wight and the mainland.
In the 1860s two huge wing batteries were added.
During World Wars One and Two the castle was fully garrisoned guarding the western entrance to the Solent.
The conservation project will centre on the wartime look-out tower, gun emplacements and searchlight position on top of the wing batteries.
English Heritage Properties Curator Roy Porter said: "We're looking at the concrete structures added around 1902 and also to the top of the castle in the 1940s
"These were thrown up in a hurry at a time of national emergency. Our job is to make these temporary structures permanent and protected for the future."
The castle will remain open to the public during the work. It is hoped the restoration will be finished by October.

Joshua, 27, and Ukraine's Klitschko, 40, had agreed terms on a world heavyweight title bout.
But Klitschko is reportedly reluctant to fight without at least one of the WBA or WBO titles on the line.
Hearn said he was "crossing fingers" that Klitschko took the fight.
Both the WBA and WBO will need to sanction the bout for their respective belts to be made available, but are yet to do so.
Britain's Tyson Fury beat Klitschko last November to win the WBA, IBF and WBO titles, before being stripped of the IBF title for failing to fight the mandatory challenger.
Britain's Joshua then beat American Charles Martin to win the IBF belt in April.
Last week, Fury, 28, relinquished his WBA and WBO belts and his boxing licence was then suspended.
The WBC belt is held by American Deontay Wilder.
"We are beginning discussions with other opponents now while crossing our fingers that Klitschko takes the fight, regardless of how many belts are on the line," Hearn told Sky Sports.
Another option for Klitschko would be to fight New Zealander Joseph Parker for the WBO belt in Germany.
"In an ideal world, there would be as many belts as possible on the line, but I hope he takes up the challenge rather than a soft touch in Germany," added Hearn.
Parents are being urged to get their children vaccinated following an outbreak of measles at a nursery school in Port Talbot.
[NEXT_CONCEPT]
Work to repair parts of a landmark castle on the Hampshire coast has begun.
[NEXT_CONCEPT]
Britain's Anthony Joshua will defend his IBF heavyweight title in Manchester on 10 December whether it is against Wladimir Klitschko or another fighter, says promoter Eddie Hearn.