Sufism or Tasawwuf is a school of thought (and not a religious sect) which exists both in the Shia and the Sunni faiths. "Sufi" is a person who believes in the principles of Sufism. Sufis in Iran are mainly Shiite.
According to The New Encyclopedia Britannica, Sufism is an aspect of Islamic belief and practice in which "Muslims seek to find the truth of divine love and knowledge through direct personal experience of God. Sufism consists of a variety of mystical paths that are designed to ascertain the nature of man and of God and to facilitate the experience of the presence of divine love and wisdom in the world." (1989, vol. 19, p. 355)
As explained in The New Encyclopedia Britannica, Sufism began in the seventh century (1989, vol. 22, p. 19). In Iran, it especially flourished during the Mongols-domination period in the 12th century. A number of Iranian thinkers and poets contributed to Sufism in the years following the Mongols occupation of Iran (Ibid.).
As an organized order in the form of fraternities, Sufism came into existence in the 11th century in Iran (The New Encyclopedia Britannica 1989, vol, 22, p. 22). However, well-established orders and fraternities emerged after the 12th century (Ibid.). The attached pages (18-24) of the same source provide additional information on Sufism.
Helen Chapin Metz claims that sufism developed in Iran in the ninth century among Muslims who "believed that worldly pleasures distracted from true concern with the salvation of the soul" (Iran: A Country Study, 1987, p. 125). Metz maintains that, in general, Sufis renounced materialism which they believed supported and perpetuated political tyranny. Over time, a great variety of Sufi brotherhoods was formed (including several that were militaristic) one of which established the Safavid Dynasty in Iran in the 15th century (Ibid.).
The same source claims that the largest Iranian Shia Sufi order is the "Nimatollahi" (Iran: A Country Study 1987, p. 125). Other important orders are the "Dhahabi" and "Kharksar" brotherhoods. Sufi brotherhoods, i.e., the "Naqshbandi" and the "Qadiri", exist among Sunni Muslims in Kordestan (Ibid.).
Metz claims that the Shia clergy have considered Sufism as deviant despite the association of Sufism with Shia ideas (Iran: A Country Study 1987, p. 125). Hence Iranian Sufis have experienced persecution by the clergy at certain periods of time. Under the late Shah, Sufism was revitalized due to the weakness of the clergy (Ibid.).
While there is no indication of persecution of Sufis by the Islamic government of Iran, the Sufi brotherhoods are regarded suspiciously and generally have kept a low profile (Iran: A Country Study 1987, p.125).
Further information on the current status of Sufism in Iran is currently unavailable to the IRBDC.
Attachments

Metz, Helen Chapin. Iran: A Country Study. Washington D.C.: Department of the Army, 1987, pp. 124-126.
The New Encyclopedia Britannica, vol. 19. Chicago: Encyclopedia Britannica, Inc., 1989; p. 355.
The New Encyclopedia Britannica, vol. 22. Chicago: Encyclopedia Britannica, Inc., 1989; pp. 18-24.