Yes, it looks strange
It's strange because it's non-standard. You could move the Search box from your mega-menu to the standard location.
Here's a list of interesting articles from the Nielsen Norman Group. It can help you decide where to put the Search box, and how to format it, for best user performance. In particular, here's a quote from this article (emphasis added):
When search is placed in an unexpected location, users need extra help to find it.
Users first look to the upper-right corner for search. If they don’t find it there, they start scanning the top of the page. Among sites that had the search icon on the left, those that used a large, empty open-text field fared best with our users. Although the users eventually found the search box, they shouldn’t have had to scour the page for it in the first place.
So: use the word Search as a label, perhaps use the magnifying-glass icon too, and place the control in the upper right corner of the page:
In the comments, below, you mention that this new Search box on the mega-menu is not for site-wide search, but for searching a limited scope. Aie! This can work if your site IA and design and your users can handle it. Read about scoped search.
And then there's the update in your question, above: a drop-down on a drop-down is non-standard, definitely strange. Look for better ways to implement this. If nothing else, use formatting to visually separate the mega-menu from the Search, and perhaps place it "above" the mega-menu, visually. These suggestions come with a clothes-pin for your nose (and mine), because my suggestions stink!
Be creative in solving this design problem
You mentioned in the comments, below, that you're not allowed to edit existing library elements. I've never let the rules stop me from trying to persuade others to reconsider. A few ideas:
- Challenge the design constraint. Use published research. Do an inventory of competing sites and other sites in general that are known to perform well.
- You mentioned in the comments that the mega-menu is a new element. I'd say you need another new element: the Search box, and element that you can place in or very close to the upper-right corner.
- If your site gets lots of traffic, introduce A|B testing. Once people have agreed to that, use this method to test different the Search box in the upper-right corner.
- I'm sure there are other possible solutions. There are always at least five!
Signalling what will be searched
Once you move Search off the mega-menu and into a standard position, that will reduce the expectation that Search will search the mega-menu. After all, people expect search results to list links to content, not links to links to content. :)
Just to be clear: this isn't a problem you should fix. It's a symptom or side-effect of a different, more serious problem. Solve the correct problem.