A majority of believers arrived from Bosnia-Herzegovina and Croatia, the local information centre said.
There were also organised tours of pilgrims from a score of countries, including Austria, Canada, China, Germany, Great Britain, Ireland, Israel, Korea, Lebanon, Mexico, Portugal, Slovakia, Slovenia, Spain and the United States.
All day, religious services are being said in 14 languages.
The central mass will be held by prominent Croatian theologist Tomislav Ivancic at 1900 hrs on Friday.
The reported apparitions at Medjugorje have not yet been officially declared "worthy of belief" by the Catholic Church.
Earlier this year, the Vatican established a 17-member commission of inquiry into this matter.
The Bishops' Conference of the former Yugoslavia concluded at a convention in Zadar in 1991 that investigations conducted at the time of the apparition did not provide evidence that the events in Medjugorje were supernatural, noting that the case should continue to be followed.
Six children from Medjugorje said in 1981 that the Virgin Mary appeared to them for the first time on 24 June that year. Almost thirty years later, some of them still claim that they see apparitions of the Virgin May.
It is estimated that more than 40 million pilgrims have visited Medjugorje since then.