It is not yet known how the plans would be applied to Jewish cemeteries, which are owned by community burial boards.
The proposals would back a period of 75 years between a burial and re-use. The nearest living relative of the person who died three-quarters of a century earlier would have the opportunity to veto the re-use of the grave.
SCoJeC said: "We are particularly concerned that arrangements that may be put in place for the effective confiscation of unused plots might result in non-Jews being buried in areas set aside for Jewish burial. This would be extremely distressing to the community."
The Catholic Church in Scotland has also opposed the plans, whereas the Protestant Church of Scotland backed the proposal.