Update
- Do
Ctrl
+ F
- Then
Ctrl
+ Alt
+ E
- Type the text to search
On MacOS, it's cmd
instead of Ctrl
Original Post
You can do it like this (mentioned keymaps are for Linux):
Let's take as an example the following code, where we will be searching for the word "key" inside the method "clear". As you can see there are many occurrences of that word (in red, highlighted the ones we want in our results, and in blue other occurrences, which we do not want to appear in our search results)

1- Select the area you want to limit the search scope to.

2- Press Ctrl+Shift+F. It will pop up a search window with the selected text pre-filled in the search box.
3- Select the options "Scope" and, in the combo next to it, "Selection" (if they are not selected by default)

4- Type the word(s) you want to search (in this example, the key
word).

5- The results shown will be limited to the selected area. Notice how there are only 9 matches in the upper right corner ("Match case" option is checked), despite in the same file there are many other occurrences of the same word.
However, I was neither able to find a key combination in order to do this as a single action nor assign a new one. Also, notice how the search includes the text in the method documentation.
Tested using IntelliJ IDEA 2018.1.4 (Ultimate Edition), Build #IU-181.5087.20 on Ubuntu 18.04