I believe you may be describing a humeral veil (velum humerale), which must be made of silk, the purpose of which is "to cover the hands when something is held in them" and "is worn like a cape over the shoulders."
It is most often seen when a Priest, garbed with a white humeral veil, holds the monstrance at a Procession or Benediction of the Blessed Sacrament.
Ceremonies of the Roman Rite Described by Rev. Frs. Adrian Fortescue and J. B. O'Connell (10th ed.; London: Burns Oates & Washbourne, Ltd., 1958), chapter ii., p. 32.
Matters Liturgical: The Collectio Rerum Liturgicarum of Rev. Joseph Wuest, C.Ss.R., (trans. Rev. Thomas W. Mullaney, C.Ss.R, ed. Rev. William T. Barry; 10th rev. ed; New York: Frederick Pustet Company, 1959), no. 130.