While we may not think of the feast of the Visitation of Mary as a Eucharistic feast, Pope Benedict XVI made the connection in an address during the Year of the Eucharist in 2005.
He first noted how St. John Paul II named Mary the "Woman of the Eucharist":
In his last Encyclical, Ecclesia de Eucharistia, our beloved Pope John Paul II presented her to us as "Woman of the Eucharist" throughout her life (cf. n. 53). "Woman of the Eucharist" through and through, beginning with her inner disposition: from the Annunciation, when she offered herself for the Incarnation of the Word of God, to the Cross and to the Resurrection; "Woman of the Eucharist" in the period subsequent to Pentecost, when she received in the Sacrament that Body which she had conceived and carried in her womb.
With this connection in mind, it is interesting how there is a tradition in some places of housing the Eucharist in tabernacles that are within statues of the Blessed Virgin Mary.
Father Stefano Manelli, in his book Jesus Our Eucharistic Love, briefly explains this tradition:
[I]n some of the churches in France, the tabernacle used to be encased in a statue of Our Lady of the Assumption. The significance is quite clear: it is always the Blessed Virgin Mary who gives us Jesus, who is the blessed Fruit of Her virginal womb and the Heart of Her Immaculate Heart.
The first Eucharistic procession
Pope Benedict XVI goes a step further and takes all of this symbolism and ties it to the Visitation of Mary to Elizabeth:
Today, in particular, we pause to meditate on the mystery of the Visitation of the Virgin to St Elizabeth...In a certain way we can say that her journey was -- we like to emphasize in this Year of the Eucharist -- the first "Eucharistic procession" in history. Mary, living Tabernacle of God made flesh, is the Ark of the Covenant in whom the Lord visited and redeemed his people. Jesus' presence filled her with the Holy Spirit.
In many ways it is hoped that any Eucharistic procession we participate in have the same spirit of joy. We hope and pray when we process through the streets that others will recognize Jesus and be filled with the Holy Spirit, just as Elizabeth was when Mary visited her.
