Any priest since the sixties. I read that somewhere.
I live close to a Benedictine monsastery and as far as I know only Benedictines can bless them. It has to do with the exorcism power of the medal.
THE BLESSING OF THE MEDAL OF ST. BENEDICT
The Medal of St. Benedict must be blessed by a Benedictine Father, or by a priest especially authorized. [The blessing can now be given by any priest (Instr., 26 Sept. 1964; Can. 1168). Also, Dom Gueranger states that the Medal is powerful even without the special Benedictine blessing. – Publisher, 1995]. There are three solemn prayers of the Church for the blessing of the Medal.
The first prayer is an exorcism of the wicked spirit, to make void his evil influence, with the earnest petition that the Medal be for the welfare of the body and soul of the wearer. The second prayer is a fervent petition:
O Almighty God, the Giver of all good gifts, we humbly beseech Thee that Thou wouldst bestow, through the intercession of the holy Father St. Benedict, Thy blessing upon these Medals, their letters and characters designed by Thee, that all who wear them and strive to perform good works may obtain health of body and soul, the grace of salvation, the indulgences conceded to us, and by the assistance of Thy mercy, escape the snares and deceptions of the devil and appear holy and stainless in Thy sight. Through Christ Our Lord. Amen
The third prayer is very impressive in virtue of the detailed and solemn commemoration of the agony, sufferings and death of Our Lord.
After the blessing, the Medals cannot be sold; otherwise, the blessing is lost. Medals must be bought before they are blessed.