Is there a word for a 'letter that should not be opened until after a specified date?'

I've seen the term Open When letter used for this sort of thing, although it's not a particularly common phrase. It can be a specific date like a birthday, a general "open when you graduate" , or "open when you're sad or lonely". The derivation of the name is obvious.

Here are a couple of crafting blogs that mention the idea:

• 50 of the Most Creative Open When Letter Ideas
• Open When Letters: 280 Ideas + Printables

Is your name Marty McFly?

Some customers are using Future Mail to send letters to their future selves, others use it to be sure their anniversary, birthday, or holiday greetings will arrive exactly on time. Future Mail customers simply fill out, address their cards, letters, or packages, and specify the date they want them delivered. These new companies will make it happen. One can even purchase gifts and flowers to be sent in the future.

When signing up for the service, customers are assessed a fee depending on how long the company has to hold on to the deliverables. Customers must also provide current contact information, in case their item is undeliverable in the future. Once the letter or package is handed over, the company tucks it away in a safe place until the date selected comes around. Though some customers have concerns about what happens to their packages if the companies fail, the service continues to catch on. — USPS: Mail to the Future?