Formal/General:
* 謎のプレゼント (nazo no purezento): This is the most literal translation, meaning "mystery present."
* サプライズギフト (sapuraizu gifuto): This means "surprise gift," which can also convey the element of mystery.
Informal:
* びっくりプレゼント (bikkuri purezento): This means "surprise present," with a bit more emphasis on the element of surprise.
* お楽しみプレゼント (otanoshimi purezento): This means "enjoyment present," suggesting that the recipient will enjoy the surprise.
Specific:
* 福袋 (fukubukuro): This specifically refers to a "lucky bag," a traditional Japanese gift bag containing assorted goods of unknown contents.
Choose the phrase that best fits the situation and the level of formality you need.