Bishop Salvatore Matano said it was to stop the spread of the deadly Ebola virus.
Five thousand people have died from the illness which is rapidly spreading across Liberia, Guinea and Sierra Leone.
Any priest who ignores the ban may be stopped from working in the diocese on their return.
"I hope this decision does not cause any grave inconvenience but the seriousness of the Ebola epidemic demands a strong and reasonable response," said Revd Edward Palumbos, the diocese director of priest personnel.
He added: "The bishop deeply appreciates your many contributions to the life of our diocese and is extremely concerned that neither you nor the people with whom or to whom you minister fall victim to this disease.
"This decision is being made purely from a pastoral concern for the people of God here in Rochester and to insure that they maintain the highest confidence in us who minister to them in Christ's name."
It's thought other Bishops in New York State could follow this rule.