No, and neither is there any liturgical discipline that anyone should be blessed by anyone, clerical or lay, at Communion time. It is a custom only that arose as a means of including in some way during Communion time those who could not, for whatever reason, receive Communion. Since it is not part of the liturgical rubrics, some parishes do not offer such blessings.
DISCLAIMER: Catholic Answers has turned over the archive to Catholic-Questions.org and no longer owns, manages, or moderates the forums. For additional apologetics resources please visit www.catholic.com.