Wood sent down five overs on the third morning in Antigua, before finally caving in to his ongoing elbow problems.
He ended up being a huge miss for England as Nkrumah Bonner's century handed the hosts a 62-run lead on 373 for nine.
With Ollie Robinson already out through injury, Wood's arrival on the sidelines only added to England's lack of bowlers.
But Ben Stokes stepped up when called upon, and sent down an impressive 28 overs for figures of two for 42.
It was a huge risk considering Stokes was expected to lower his bowling responsibilities ahead of the West Indies Test, with the 30-year-old slowly recovering from a side strain.
Still, when Wood was withdrawn, Stokes shouldered more than his fair share and became England's standout bowler.
Stokes' mentality pleased England head coach Paul Collingwood, who described him as a "warrior".
"It's fair to say that he declared himself fit to bowl in this first innings.
"None of us were expecting that many overs out of him. Obviously we had to be pretty cautious with the approach, but, Ben being Ben, he wants to be in the competition.
"When you lose overs from somewhere else, he'll want to make overs up. He's a battler. His attitude has been absolutely superb and he's shown today what kind of a warrior he is. That's what sort of character he is. He wants to put his body on the line all the time."
Collingwood also seemed dismissive of Wood's chances of returning to the fold for the second innings, meaning England may have to risk Stokes bowling again.
"It's pretty sore at the moment. We're going to have to assess him overnight and see if he is going to be available for the second innings," said Collingwood.
"All I know at this moment is it's soreness in the elbow. He didn't feel that confident this morning and then he got it strapped up and bowled a good spell for us. When he tried another over it didn't feel good."
However, aside from England's injury problems, Collingwood was pleased with what he saw from his side during his first Test as head coach.
England struggled to create chances in what turned out to be a slow, grinding third day, but Collingwood had no concerns with the attitude shown by his team.
"I thought today was probably one of the best efforts I've seen in an England shirt in Test cricket," he said.
"The attitude in the field was exceptional. It was tough, hard work out there. It's a placid pitch, a docile pitch."
The first Test resumes on day four at 14:00 GMT on Friday, March 3.