The left-back earned his second caution late on for remonstrating with Godfrey Sekopo, just after the referee had blown in Bucs' favour at Free State Stadium.
Cloete is now suspended for Wednesday's clash with Golden Arrows, as well as for the first game of the New Year against Black Leopards (both at Orlando Stadium) on 15 February.
"I am feeling bad about the red card, it was in the heat of the moment and now I have to watch my teammates play in the last match of the year at home against Golden Arrows and during our first game of the New Year against Black Leopards," Cloete told his club''s official website.
Pirates boss Julio Leal may employ either Lucas Thwala, Lizo Mjempu or Sibusiso Mxoyana at left-back against Arrows after experimenting with the duo in training on Monday.