Having been knocked out of the FA Cup at the fourth-round stage by Chelsea, Stoke opted to make the most of a rare 10-day gap between fixtures by heading to the United Arab Emirates.
However, Assaidi was injured during a training session and is now facing a spell on the sidelines.
Stoke have yet to confirm how long the Moroccan will be absent for, or if he will return to parent club Liverpool prematurely, but the 25-year-old is expected to be unavailable for a number of weeks.
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"He got a block tackle in training and just opened up his knee ligaments, so he is going to be out of action for a little while.
"We obviously hope that he is going to be back sooner rather than later, but it is one that we will just have to wait on unfortunately.
"Apart from that negative it was a good time away, and the quality of work that the lads produced was really encouraging."
Stoke, three points outside the Premier League relegation zone in 14th, travel to title-chasing Manchester City on Saturday and can take heart from a positive update on the fitness of defender Robert Huth, who has been sidelined for three months with a knee problem.
"Robert joined in over there (in Dubai), and he is training as part of the group again today (Thursday), which is really encouraging," added Hughes.
"We are trying to push him on a bit further now, because we have had to take our time with him after having a few initial setbacks.
"I think those were more to do with Robert's enthusiasm to get back as soon as possible, so because of that we have had to take a couple of steps back to progress him at the right rate.
"He is now starting to cope with the work we are asking him to do, which is encouraging, and hopefully we can step him up again now."