Cambridge dictionary describes woes as
big problems or troubles:
- The country has been beset by economic woes for the past decade.
- Unusually poor harvests have added to the country's woes.
Injury woes could indeed be coined injury problems or injury setbacks as stated by Fumble Fingers in the comment in reply to OP's question.
The phrase is mainly used in sport as mentioned by OP, particularly in football. It refers to the difficulty teams have in creating optimized player squads because of the number of unavailable players recovering from their injuries.
It could be used in allusion to "woe is me"
said to express how unhappy you are:
- I'm cold and wet and I don't have enough money for the bus home. Oh woe is me!
A recent article referring to an update on Tottenham Hotspurs'midfield injury woes quotes manager Mauricio Pochettino, as saying he
is confident injuries to Mousa Dembele and Erik Lamela are minor amid fears of a crisis in his midfield.
Central midfielders, Eric Dier and Dembele, have been vacationing during Spurs’ pre-season tour in America due to their World Cup exploits, while Harry Winks and Josh Onomah stayed at home to nurse injuries.
Victor Wanyama, Moussa Sissoko and 18-year-old Tashan Oakley-Boothe have all sustained injuries during Spurs’ preparations ahead of the new season, which could potentially leave Pochettino without seven central midfielders when they face Newcastle in their opening game of the 2018-19 Premier League season on 11 August.
Another football related article referring to the South African national football team - Baxter bemoans Bafana Bafana injury woes says
“We’ve already got Bongani Zungu and Themba Zwane out‚ we’ve got Keagan Dolly out‚ and then you bring in a Morena who I thought really was perfect for this game. And then he pulls a hamstring‚” Baxter said after training Steyn City School in Fourways, Johannesburg.
“And then you’ve also got Vincent Pule‚ who’s got a bad one. The scans showed that he’s got damage on is cruciate ligament. So it isn’t just a kick‚ as people might have first thought.
“Those were two withdrawals that caused a little bit of concern.
“But the lads we’ve brought in – Mkhize will arrive later‚ and Lorch is here – will add cover.
“The other one not here is Dino Ndlovu. His flight was cancelled in Hong Kong. He very professionally sent me a video of the board where it was actually saying in Chinese‚ and then it flicked over‚ that he was delayed.
“So that’s not ideal either – he’s only going to have two days’ preparation.
“But again‚ we’ve got Percy Tau who can play No.9 – we’ve got the big lad [Lebo Mothiba]‚ who’s looking very good.”