There are three issues to be addressed in this instance. First, only a validly ordained priest in the Catholic Church who is in good standing may offer the Holy Sacrifice of the Mass. Therefore, a non Catholic minister cannot concelebrate the Eucharistic Liturgy with the priest.
Second. Normally, a marriage between a Catholic person and a non-Catholic person is celebrated outside of Mass. Communion is an essential part of the Mass and a symbol of unity of those participating in it. Although in marriage the two become one flesh, they are not one in the area of religious affiliation. This religious separation does not need to be accentuated by one spouse receiving Eucharist while the other does not.
However, if the circumstances justify it, a marriage between a Catholic and a baptized non-Catholic can be celebrated within Mass, subject to the local bishop’s consent and respecting the Church’s law regarding to reception of the Eucharist.
Third, the Catholic priest may however, invite the minister to participate in the celebration of the marriage, to read from the Scriptures, give a brief exhortation and bless the couple.