The German word for surprise is "Überraschung" (with the verb being Überraschen). But let's talk about something a bit more specific: Ich wundere mich is a German phrase English-speakers frequently use to express “I wonder” but more often actually means “I am surprised/puzzled/mystified/amazed/astonished”. To express the concept of “I wonder” Germans would rather use Ich frage mich:

Examples

Ich wundere mich dass es so kalt ist. I am surprised that it’s so cold.

Ich frage mich warum es so kalt ist. I wonder why it’s so cold.

Ich wundere mich dass sie mich mag. I am amazed that she likes me.

Ich frage mich ob es eine gute Idee wäre. I wonder whether it’d be a good idea.