Swift was stretchered from the field in the first half against Wakefield with a left leg injury.
Saints defeated the Wildcats 44-4 at Langtree Park.
Swift could be out for some time and Cunningham wants the RFL to investigate these kinds of tackles, which have already seen the likes of Mark Percival and Michael Shenton out for long periods this season.
“It’s a leg injury, another of those drop on the back of the leg,” he said.
“Something happens, it’s something the RFL needs to look at, the way we defend and how we put pressure on certain parts of the lower limbs.
“It’s not looking good for Swifty. Anything that’s less than a long period will be good for us.”