The dreadful surprise that Montag suddenly becomes aware of is the fact that he is going to have his house burned down. The words "dreadful surprise" are spoken by Captain Beatty. He says them to Montag when they get to Montag's house and Montag realizes what is going on.
Beatty says to Montag that is is a surprise to find out that something is happening to one's own self. We always think bad stuff will happen to others, but this time it really is happening to Montag and that is Montag's dreadful surprise.