The left-hander missed England's hit-out at the Floreat Oval in Western Australia to receive treatment on his back while fast bowler Stuart Broad also sat out the session with a similar problem.
"I'm sure he'll be fine," England's top-order batsman Ian Bell told reporters. "He's had the odd little niggle with the back, which I suppose we all have certain areas we have to keep working on.
"Obviously a long flight isn't always easy. I'm sure he'll be right in the next week or so."
Cook is expected to sit out of the visitors' first three-day tour match against a WA Chairman's XI, starting at the WACA Ground on Thursday.
England, who won the first of the back-to-back Ashes series 3-0 at home, will play two more warm-up games before the opening Test of five against Australia starts at Brisbane on November 21.
For the hosts, George Bailey, currently leading Australia in a one-day international series in India, moved into prime position to secure a call up to the Test team after he missed out on a spot in the 'A' side to face England next week.
National selector John Inverarity said they would prefer the in-form batsman to face Australia paceman Ryan Harris in a domestic match against Queensland starting on the same day.
"We thought George had gone past that, that's more development and he was firmly entrenched as an Australian player," Inverarity told reporters.
"He's a very mature, calm young man. Composed, and I think you'll see in his batting performances, a difficult situation brings out the best in him."
The 31-year-old Bailey averages more than 53 in 33 ODIs for Australia but is yet to make his Test debut.
"When we look at a player, we look at four things," Inverarity added. "Their batting, their bowling, their fielding and their character - or what else they bring to the team.
"And George certainly brings a great deal in that character category to the team. His performance in ODI cricket has been outstanding.
"Since he started 18 months ago, he's been our best performed one-day player, in terms of average runs, aggregate and strike rate."
Australia Test captain Michael Clarke said he would be "extremely happy" if Bailey got the nod for a middle-order spot in the Ashes side.
"Bailes has done an exceptional job in the last couple of years in the shorter formats and he's leading the boys really well," Clarke said.
"It's obviously going to come down to performance and who selectors think the right man is for that position but I've always enjoyed playing alongside Bailes, he's a great fella and if they select him I'll be extremely happy."
- Sports & Recreation
- John Inverarity
- Western Australia