It is "impossible" for God to "bless sin", the Congregation for the Doctrine of the Faith (CDF) said on Monday.
But the CDF did note the "positive elements" in same-sex relationships.
In October, Pope Francis said in a documentary that he thought same-sex couples should be allowed to have "civil unions".
In the Catholic Church, a blessing is given by a priest or other minister in the name of the Church.
On Monday, Pope Francis approved the response by the CDF, saying it was "not intended to be a form of unjust discrimination, but rather a reminder of the truth of the liturgical rite".
Some parishes in recent months, including in Germany and the US, have started giving blessings to people in same-sex relationships as a way to welcome gay Catholics to the church, Reuters news agency reported.
The CDF's response was in answer to the question posed to it: "Does the Church have the power to give the blessing to unions of persons of the same sex?". It replied: "Negative".
The CDF noted that marriage between a man and a woman is sacrament and therefore blessings cannot be extended to same-sex couples.
"For this reason, it is not licit to impart a blessing on relationships, or partnerships, even stable, that involve sexual activity outside of marriage (i.e., outside the indissoluble union of a man and a woman open in itself to the transmission of life), as is the case of the unions between persons of the same sex," it said.