Johnson won all five of his matches in the United States' record 19-9 win over Europe at Whistling Straits last year, but may not appear in the biennial contest again going forward.
PGA of America chief executive Seth Waugh said last year: "If someone wants to play on a Ryder Cup for the US, they're going to need to be a member of the PGA of America, and they get that membership through being a member of the (PGA) Tour."
Speaking at a press conference ahead of the inaugural LIV Golf event at Centurion Club, two-time major winner Johnson said: "I resigned my membership from the Tour and I'm going to play here, for now. That's the plan.
"What the consequences are going to be I can't comment on how the Tour's going to handle it. I can't answer for the majors but hopefully they're going to allow us to play.
"Obviously I'm exempt for the majors so I plan on playing there unless I hear otherwise.
"All things are subject to change. The Ryder Cup is unbelievable and has definitely meant a lot to me. I'm proud to say I've played and represented my country and hopefully I will get a chance to do that again, but I don't make the rules."
Graeme McDowell, whose Ryder Cup eligibility is tied to membership of the DP World Tour, said he had not felt the need to resign from the PGA Tour, although he admitted he did not want to get involved in a "legal situation" with the organisation.
"In regards to the Ryder Cup, it's something I weighed up long and hard before I made the decision to come out here. I hope it doesn't affect that," said McDowell, who holed the winning putt at Celtic Manor in 2010.
"When you look at the European Tour and the players here have done a great amount for the Ryder Cup product and it would be a shame to see those guys not invited back.
"Is it healthy for the sport? This Tour is designed to be an add-on to the greatest tours in the world."