No, the non-Catholic may not receive Communion at a Catholic wedding. Actually, not all Catholics may receive Communion. Only those who are in a state of grace can receive the Eucharist. To receive Communion in the Catholic Church is a sign of complete acceptance of Catholic teaching. It is also a sign of complete unity among believers. Unfortunately, Catholic and non-Catholic Christians still do not share such unity. At present, the mutual reception of Communion by Catholics and non-Catholics would not be an honest sign. Because of the inability of non-Catholic Christians to receive Communion, Catholics who are marrying a non-Catholic are usually encouraged not to have a Mass as part of their nuptial liturgy.