In my opinion, both sentences are correct in grammar.
However, they do have difference in the meaning. I try to make it easier to be understood using scenes.
For example, there should be a meeting holding in this afternoon.
1. The meeting was postponed until next week.
This sentence can be used, if a official notification has been made some time before and you are now sure that the meeting will not be held until next week. It used a past tense as the informing of "Postpone" is happened.
2. The meeting will be postponed until next week.
If this sentence is used, then the situation could be:
You knew from some unofficial sources that your boss is planing to hold the meeting in next week, but he has not yet informed you and your colleagues formally, which equals to "The date is to be decided" in official occasion (But you know that he is going to make the notification.) Then, the "Postpone" is now a future tense, as it has not been informed and there is a possibility that the informing will not be happened ( if the boss changed his mind).
Hope these help. =)