Using condoms to avoid pregnancy can be acceptable in difficult situations, he said during a press conference.
He referred to the time when Pope Paul VI permitted nuns in Africa to use contraception when they were at a high risk of being raped.
Zika has been spreading across parts of South America and has been connected with birth defects in children.
The virus is most prevalent in Catholic nations like Brazil.
Francis confirmed the Church's stance on abortion, though, saying it was "evil".
"Do not confuse the evil of avoiding pregnancy in and of itself with abortion," he told reporters.
"Abortion is not a theological problem. It is a human problem, a medical problem. You kill one person to save another."