The vote came at the end of a Vatican assembly on the Amazon, where there is a severe shortage of priests.
For the proposal to take effect, it must be backed by Pope Francis, who is due to make his position clear soon.
Traditionalists fear a slippery slope to married priests throughout the Church, diluting its unique character.
The vote was taken at a three-week assembly, known as a synod, of some 180 bishops in Rome. It also looked at the role of women in the Church's work, and environmental issues.
The Catholic Church is the oldest institution in the Western world, tracing its history back almost 2,000 years, and counts more than a billion members.
Why are priests so scarce in the Amazon?
Residents of least 85% of villages in the region cannot attend Mass every week, Reuters news agency reports.
"Sometimes it takes not just months but even several years before a priest can return to a community to celebrate the Eucharist, offer the sacrament of reconciliation or anoint the sick," the synod document says.
Three out of five bishops at the synod came from the nine Amazon countries, AFP news agency notes.
How would the change be justified?
Under the synod's proposal, passed by 128 votes to 41, married "men of proven virtue" could join the priesthood in remote parts of the region.
Advocates of the change argue that it would not be a reversal of the rule on celibacy for priests but an exemption, like that already given to married Anglican clerics who convert to Catholicism.
"Legitimate diversity does not harm the communion and unity of the Church, but expresses and serves it," the synod's final document says, as quoted by the Catholic News Agency.
Speaking at a press conference at the end of the synod, the Archbishop of Benevento, Cardinal Michael Czerny, explained the decision: "Things have to change.
"We cannot keep repeating old responses to urgent problems and expect to get better results than we've been getting so far."
Pope Francis is expected to issue his guidance on the issue by the end of the year.