I believe it can also be done by an Extraordinary Minister of Holy Communion or deacon as well as a priest.
If Communion under both kinds is permitted, then this method is permitted. This was made clear in the 2004 Instruction Redemptionis Sacramentum:
“[103.] The norms of the Roman Missal admit the principle that in cases where Communion is administered under both kinds, “the Blood of the Lord may be received either by drinking from the chalice directly, or by intinction, or by means of a tube or a spoon”.[191] As regards the administering of Communion to lay members of Christ’s faithful, the Bishops may exclude Communion with the tube or the spoon where this is not the local custom, though the option of administering Communion by intinction always remains.”
The method of receiving by intinction is explained in the the 2002 General Introduction to the Roman Missal (GIRM) which can be accessed from
romanrite.com/girm.html :
“287. If Communion from the chalice is carried out by intinction, each communicant, holding a communion-plate under the chin, approaches the priest, who holds a vessel with the sacred particles, a minister standing at his side and holding the chalice. The priest takes a host, dips it partly into the chalice and, showing it, says, Corpus et Sanguis Christi (The Body and Blood of Christ). The communicant responds, Amen, receives the Sacrament in the mouth from the priest, and then withdraws.”