According to the Mishna (52b) a portion from an animal that was brought as a sacrifice in the Temple cannot be used as kesef kiddushin. This is true for both kodashei kodashim – sacrifices like a sin-offering where the meat is given to the kohanim – as well as for kodashim kalim – sacrifices like a korban shelamim, where the meat is divided between the kohanim and the owner of the sacrifice.
The Gemara explains that this rule is derived from a passage in Bamidbar (18:9) that compares the meat of the sacrifice that is given to the kohanim to fire; just as fire is only for eating, similarly the meat of the sacrifice is only for eating. This enigmatic statement is explained by Rashi to mean that the portion given to the kohen is paralleled to the portion placed on the altar to be burned. Just as the portion belonging to the altar must be “eaten” – i.e. burned – so the portion given to the kohanim must be eaten, and it cannot be used for any other purpose.
Rashi appears to expand the rule of the Mishna not only to kohanim, but also to the owners of the sacrifice. That is to say, the owner of the korban would not be able to marry a woman with his portion of the korban that is given to him to eat. Others disagree with Rashi, arguing that the Mishna only restricts use of the sacrifice to kohanim, but that the owner of a sacrifice would be able to make use of his portion. The Talmud Yerushalmi raises the question of whether the restrictions apply only to someone who wants to use the meat itself for kiddushin, or would it also apply to someone who attempts to use the value of the meat to effect the kiddushin, giving the meat to a woman who can then sell it to a kohen and receive money in exchange. Tosafot, who assume that even the value of the meat cannot be used, explain that since the meat from a sacrifice is seen as being a divine present (mi-shulhan gavo’ah ka-zakhu), even its value cannot be used for mundane purposes.