The 18-year-old, who is regarded as a future first-team player at the Black Cats, is expected to be on the bench for Tuesday's clash against Preston North End.
Barker told the club's official website: "We are delighted to have Johnny on board. He has been training for a few days with us and you can see that he has all the attributes to develop into a good goalkeeper.
"He is working with Sunderland's first-team squad and has been a regular in their Academy team. This will give him more experience and, of course, provide us with cover for Paul Jones."
Experienced stopper Michel Kuipers departed Crawley last week.