It is a familiar, sad story for Oxlade-Chamberlain, who pulled up during the 2-0 victory over Crystal Palace in Singapore.
The Englishman had played through a planned 30 minutes in the previous friendly against Man United, but was forced off a minute before half-time just three days later.
After a largely injury-free campaign that saw him play 29 times before falling out of favour entirely at the end of January, Oxlade-Chamberlain was determined to make his mark in pre-season.
Instead, the 28-year-old is now facing a lengthy spell on the sidelines.
“With Oxlade, it will take longer,” Klopp told reporters ahead of the Community Shield clash with Man City.
“It’s a serious hamstring injury and it will take longer.
“It’s a hamstring, we all hate this word, we hate the injury, but it happens from time to time and now Ox was the one.”
The manager did reveal, at least, that Oxlade-Chamberlain would not require surgery.
However, Klopp did give an insight into Kelleher’s groin strain, with there a sense of frustration at the medical staff within the Republic of Ireland setup as he faces up to three more weeks on the treatment table.
“Caoimh felt something after the international game and everybody told him, the medical department there, it’s fine, it would be good,” he explained.
“After holiday he came back, first training, felt it again. We checked it and it was not good.
“I think Caoimh will be another two, three weeks and then should be fine.”