There are 2 ways.
Either have a Map class which is the main JPanel, to maintain the collection of units, but keep the Unit class as non-Swing. When the Map's paint() method is called, ask each Unit to redraw itself by calling a method in each visible Unit. The Unit could be inherited from any base class, for example Rectangle, or some other data structure you use in the program. In this case, the Unit class handles painting and calculations, but the Map handles the clicks and events for each Unit. It could pass the message on to the Unit if needed; however, if the unit itself doesn't need to know about these things, this method works well. The Unit class is light and economical. You can also decide whether the Unit knows its position in the Map or not.
Or have each unit as a JComponent, and handle its own events separately. The disadvantage is that each instance of a Unit creates a pile of data for drawing it as well. So if you have hundreds of units, only a couple of which are drawn, this way is not efficient. The advantage is each unit can handle its own GUI events without translation etc. This assumes also a 1:1 mapping of actual units in the game and graphical units on the screen. Also it is trickier to implement certain event handlers in the Unit, if a Unit needs to know about what other Units are around!
A third and arguably better way is to have a purely data Unit class, containing the game information about the unit, as in (1), but which has a method to create the JComponent when needed. The JComponent could, for example, be an inner class in the Unit - it could then access the Unit data. This is great if a unit may need to be displayed in 2 places (e.g. on 2 screens or views).
--
Addendum to address comments
That is correct, in (1) the Map (main JPanel) implements the mouse handler, and asks each unit in turn if it is 'hit'. This allows you to do more complex things, such as have 2 units overlapping/on top of each other, and both could respond to the click.
Also, for example, they may not be rectangular, or may be drawn with an alpha channel (if the Units were JComponents, they will by default grab any mouse event over their whole rectangle, to themselves). If your units don't overlap and are in their own rectangles, then JComponent's own mouse handler is enough.
If you use approach (1), the Map can ask each unit whether it contains a clicked point, and the Map can then handle the 'selection' process. Remember, a unit on its own won't be able to work out what other units are selected - selection may involve deselecting another unit. In that case, the selection operation is really a Map operation, not a Unit operation, although it may change the appearance or function of the Unit as well.
If you use separate JComponents for the Units, you can override contains(Point) to determine if the mouse hits the item, but this won't let other Units also respond to the click. But each Unit could 'select itself' (set a flag used when drawing) then notify the Map (it will need to find it using getParent or by a preset property).
Key things you need to know before deciding on this design would be:
Will you ever need more than one 'Map' panel per game?
Will you ever need more Unit objects than are to be displayed?
Will you ever need to display a Unit more than once?
If the answers are yes, you should separate the 'Data' classes from the 'View' classes, as suggested in 3.
then: What does a Unit need to 'do' and what does it need to know about the Map and other Units in order to do this? e.g. moving is usually done by the Map class in this situation, as it depends on the Map and on other Units; drawing is best done by the Unit because there may be many unit subtypes with different data structures that may need to be drawn; Unit selection operations as you have pointed out lie somewhere in between. If you see how Swing implements this (e.g. ButtonGroup, ListSelectionModel), the 'selection' itself can be though of as a separate class.