Use the AWS Application Load Balancer, which does Path Based Routing. That second link is a tutorial how to do it.
In short, you set up your ALB as normal, then follow these steps (copied from the AWS tutorial):
On the Listeners tab, use the arrow to view the rules for the listener, and then choose Add rule. Specify the rule as follows:
For Target group name, choose the second target group that you created.
For Path pattern specify the exact pattern to be used for path-based routing (for example, /img/*). For more information, see Listener Rules.