The ruling, which can be appealed, puts pressure on Italy to change its law and several Italian politicians renewed their calls for a change in the laws on assisted reproduction.
The Strasbourg-based court ordered the Italian government to pay the couple 17,500 euros ($21,900) in damages and expenses.
Under Italian law the only alternative for the couple was to conceive a child and abort the fetus if it was found to have cystic fibrosis, which they have already done once.
The couple found out that they were carriers of the disease after their first child was born with it. They want to have a second child by IVF so that the embryo can be screened and aborted if it also has cystic fibrosis.
They brought the case before the European court because predominantly Catholic Italy is, together with Austria and Switzerland, one of the rare European countries that has a ban on screening embryos before they are implanted.
The Italian government sought to justify the ban on the grounds that it was needed to protect the health of the mother and child and avoid the risk of eugenic abuses.
Antonio Di Pietro, head of the opposition Italy of Values party said the "resounding rebuff" delivered by the court showed Italy needed a new law that would allow analysis of embryos.
"That is, one which gives the right to have preliminary genetic analysis of an embryo not just for sterile couples but also to fertile couples suffering from hereditary diseases such as sickle cell anemia and cystic fibrosis," he said.
($1 = 0.7990 euros)
(Reporting by Gilbert Reilhac; Additional reporting by James Mackenzie in Rome; Writing by Leigh Thomas; Editing by Louise Ireland)
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