From the Anabaptist network comes the following:
Tertullian (145-220) of North Africa in his De Corona is the first Church Father to indicate that footwashing was practiced in his time, but he gives no clue as to by whom or how. Ambrose of Milan (340-97) states that it was not the practice of the Roman Church, but endorses it as a symbol of sanctification. Augustine mentions it as being rejected by some. Knight (p. 816) says flatly that footwashing always remained ‘a purely local peculiarity, introduced at an early date into some parts of the Catholic Church, but never universal’. Among the monks in particular, the hospitality custom of footwashing was widely practiced, and often in the name of Christ, but not as a universal ordinance of the church. For the monks the observance was often intended to express humility. St. Benedict’s Rule (529) for the Benedictine Order prescribed hospitality footwashing in addition to a communal footwashing for humility.
R.L. Vaughn's monograph on the history of the practice of footwashing among Baptists credits John Christopher Thomas's work Footwashing in John 13 and the Johannine Community for adding substantially to the body of knowledge regarding the practice of footwashing in the church. Vaughn says,
Thomas finds few very early references, though he makes a good argument on pp. 146-47 that the absence of such references is not proof that it was not practiced. He finds a possible allusion to feet washing in the Martyrdom of Polycarp , written in 156. He cites it according to the translation of C. C. Richardson in Early Christian Fathers (p. 154 New York: MacMillan Press, 1970).
Thomas includes an excerpt from Richardson's translation of Martyrdom:
“And when the funeral pile was ready, Polycarp, laying aside all his garments, and loosing his girdle, sought also to take off his sandals,--a thing he was not accustomed to do, inasmuch as every one of the faithful was always eager who should first touch his skin.” – 13:2 (Roberts-Donaldson Translation) http://www.earlychristianwritings.com/text/martyrdo
This above is definitely not a clear reference. Thomas points to the possibility of an allusion to feetwashing based on the description of laying aside of garments, the mention of not removing the shoes in relation to touching his skin, that apsetai
(translated touch) in some contexts means to wash, and tradition of Polycarp's connection with the Apostle John.
Thomas (passim) then quotes extensively from The Mennonite Encyclopedia, Vol. 2, Bender, Gingerich, Krahn, Smith, editors, Scottdale, PA: Mennonite Publishing
House, 1956, p. 348, and in short, cites the following church fathers and Post-Nicene writers who in their various writings at least mention the practice of footwashing in the Christian church:
St. John Chyrsostom (347-407)
John Cassian (360-435)
Pachomias (writing in ca. 404)
Casesarius of Arles (ca. 470-542)
In conclusion, while footwashing is mentioned as being in existence from the time of the apostles, on, including Paul's reference to widows who washed the saints' feet (1 Timothy 5:10), the exact nature and practice of footwashing in both social and eccelsiastical settings is imprecise at best.
Nevertheless, footwashing in an ecclesiastical setting was practiced (and still is) by such Christian groups as the Anabaptists and later the Menonnites. Other Christian denominations to this very day may engage in footwashing from time to time, not as an ordinance but as a demonstration of humility and servant-leadership.
My own local congregation within the C & M A denomination enacts the footwashing paradigm periodically, especially when new elders are installed as church leaders and under-shepherds. This meaningful ritual signifies that true elders have the privilege of serving their fellow parishioners humbly, much as the Lord himself who "came not to be served, but to serve." The primary difference in their humility: only the Lord Jesus was worthy to give "his life as a ransom for [the sins of] many."