Microsoft has recently redesigned Search Box to a new location in Office 365 Apps. At the top of your Office 365 Apps on Windows, you'll find the new Microsoft Search Box.

This new search box can be removed from the top of Office 365 Apps except for Outlook.
To remove the search box from Office 365 Apps please follow the below instructions:
To do that go to File > Options and select Collapse the Microsoft Search box by default.
With the Search box collapsed you can still access it by clicking on the Magnifying glass towards the right side of the title bar, or by pressing ALT+Q.