Any injury to Wood would be a huge worry to England given his record.
He has not played a Test since August 2024, when he was ruled out of the rest of that year because of an elbow injury.
He returned in white-ball cricket at the beginning of this year but sustained a knee injury at the Champions Trophy which subsequently required surgery.
The hamstring problem is in the same leg on which Wood had the knee operation.
The tour match against the Lions was Wood’s first cricket of any kind in nine months and his first in whites for 15 months.
Still, on a slow pitch he was immediately up to high pace, hitting 91mph in his first spell.
The England selection for the tour game appeared to hint at their plans for the first Test, with Wood part of a five-man pace attack and frontline spinner Shoaib Bashir playing for the Lions.
In recent years spin has played a diminished role in Tests in Australia, and Optus Stadium, the venue for the first Test against Australia starting on 21 November, is particularly suited to seam.
Another England pace bowler, Brydon Carse, missed the first day of the tour match through illness but is expected to join the game in the coming days.
Stokes, playing for the first time since suffering a shoulder injury in July, took two wickets in each of his three spells.
Opener Ben McKinney, England white-ball batter Cox, 17-year-old Thomas Rew and Ashes seamer Matthew Potts made half-centuries for the Lions.
Potts was dismissed by what turned out to be the final ball of the day, discomforted by a Jofra Archer bouncer. It means England will begin their reply when play resumes on day two.
“It was a decent day out,” said Brook. “It was good to get out there, put some miles in the legs and for the bowlers to bowl a few spells.
“We haven’t spent much time together, so to get back together as a group, get out on the pitch and work towards 10 wickets was a successful day.”
