Woods has withdrawn from The Masters at Augusta next week as he continues to struggle in his rehabilitation from surgery on nerve damage in his back.
He is not expected to return to action until the middle of the summer, leaving his qualification chances for the September event in jeopardy, but Watson has promised that the 14-time Major champion would be the recipient of one of his wildcard picks if he fails to secure his place automatically.
"I've been asked a little bit about, 'What if he doesn't make the team?'" Watson told reporters. "I'll pick him for the team. I just hope he gets well and starts to play again without pain. That's all that matters.
"Everybody's been in pain before, every golfer. For some, it's ended their careers. For others, they've beat it and corrected with surgery. Obviously I hope this is corrected with surgery.
"Obviously, I hope that he can recover and again swing the club without any pain."
Woods has won 48% of the Ryder Cup points that he has competed for since debuting in 1997.