IntelliJ IDEA lets you manage your imports in Scala the same way as it does for Java.

You can configure the improrts in the Settings.

Project Settings
Scala Imports

IDE Settings
Auto Import

Insert imports on paste - use this drop-down list to define how IntelliJ IDEA will insert imports for pasted blocks of code, if they contain references to classes that are not imported into the target class. The available options are:
All - select this option to have IntelliJ IDEA automatically add import statements for all classes that are found in the pasted block of code and are not imported in the current class yet.
Ask - if this option is selected, when pasting code blocks, IntelliJ IDEA will open a dialog box, where you can choose the desired imports.
None - select this option to suppress import.
If you skip an import suggested in the Ask mode or choose the None mode, the non-imported classes will be red-highlighted and an import pop-up window will appear to help you create import statements using the Alt+Enter keyboard shortcut.

Optimize imports on the fly - select this check box to have the Optimize Imports operation automatically performed for your files.

Add unambiguous imports on the fly - select this check box to have IntelliJ IDEA automatically add imports that can be added without user intervention.