Wood missed an entire session, bowling just five overs before lunch after appearing to injure his elbow.
Nkrumah Bonner scored a marathon hundred in Antigua as the hosts took a lead over England's first innings with the bat.
England's frustrations were elevated by concerns over Wood, their fastest and most in-form bowler.
The 32-year-old, whose right arm was heavily strapped, now faces an uncertain role in the remainder of the match.
Wood's injury is not entirely new. He bowled a lot of overs across four Tests in the Ashes and, before this tour, he had an injection to manage the pain it caused.
Having controversially overlooked James Anderson and Stuart Broad for this tour to empower others, England are now facing a potentially awkward shortage of quicks.
Uncapped duo Saqib Mahmood and Matt Fisher are the spare pace options, but England may soon have to consider flying in reinforcements.
Anderson hoping for recall
Anderson, who turns 40 in July, is refusing to call time on his international career and is hoping to be selected for the summer.
However, if the injury crisis continues in the West Indies, then he may be returning sooner than expected.
"I'm praying this isn't the end," said Anderson in February.
"But if I never play for England again, I know I've got amazing people around me to support me and that's really important."
"I've got one more go at digging deep," he added. "I've got a lot left to offer - I've still got the hunger and passion to play."
"It was a shock and a disappointment to get that call but having processed it, it's important I try to focus on stuff I can control and that's showing people what I can do with the ball in my hand."