Donald sustained the problem on the last round of the US Open
Luke Donald has not given up hope of making Europe's Ryder Cup team in September despite a wrist injury.
He picked up the injury during the US Open but has opted not to have surgery as he bids to make Nick Faldo's side.
"Surgery is an option but for the long term I think therapy is the most sensible route for me," said Donald.
"I'm hopeful I might have a chance to make myself available for Valhalla, but it's still too early to say," he told his golf club manufacturer's website.
Donald is 10th on the Ryder Cup world points list where only the top five players automatically qualify, but if he recovers he could be one of Faldo's two wildcard picks in Europe's 12-man team.
"Nick Faldo and I have been in contact and he's well aware of my situation," added Donald, who has not played since last month's US Open at Torrey Pines. "Obviously I hope he keeps me in mind. He'll be the first person to know if the wrist improves."
He has been diagnosed with a subluxation of the Extensor Carpi Ulnaris (ECU) tendon in his left wrist, which is a partial dislocation.
Faldo, Europe's captain for the event in Valhalla, has admitted he faces a tough decision as to whether to include Donald.
"He would need to be a pick and to pick a man who is injured would be a tough call," Faldo told BBC Radio 5 Live.
"I need to talk to him in a month's time to get an honest opinion."
"He would need a very quick recovery to get to the American PGA and to be able to play for a couple of weeks. Luke is at best going to get one or two events but he is a good balanced guy who would give me a honest opinion.
"He will be missed, but we will make up a 12-man team and will be all right."
Faldo has conceded that with the likes of Open champion Padraig Harrington and Colin Montgomerie currently out of the automatic qualifying positions, he could face some awkward decisions over his captain's picks.
"When you see how many big guys are outside at the moment, it shows you the level everybody else is playing at," he added.
"Over the next two months I will be observing how these boys respond to the challenge, that mad scramble to get inside, or close to, that top 12.
"Then we will see where I go with my picks from there."