Root also appeared to incur a calf problem.
But with England needing to win their two remaining group matches against New Zealand on Tuesday and Australia the following Saturday to guarantee a place in the semi-finals, coach Trevor Bayliss is unlikely to stomach too many more failures.
Going into the match, Bangladesh would be brimming with confidence as they have won four of their last seven ODI games versus England.
Earlier, Tamim Iqbal’s superb hundred helped take Bangladesh to 305/6, the left-hander receiving excellent support from Mushfiqur Rahim (79) in a third-wicket partnership of 166.
Woakes, a key member of England’s one-day worldwide side, managed just two overs with the new ball against the Tigers before going off with a left side strain and played no further part in a match where the all-rounder was not required to bat.
An unbeaten 133 by a cramping Joe Root, a 95 by opener Alex Hales, and an unbeaten 75 by Morgan paced an aggressive England to what, in the end, was a comfortable win in sunny conditions. That record is likely to be broken at least once in this tournament, though, as one-day cricket has transformed in recent times. In fact, he only hit six boundaries on way to his 100, and accelerated after reaching the triple figures.
England’s Chris Woakes has been sent for a scan on a side strain and is a “worry” for the rest of the Champions Trophy, says captain Eoin Morgan.
Roy looked jittery throughout his eight-ball innings and his dismissal epitomised that. The under-pressure opener was caught at short fine leg attempting a ramp shot with just one run to his name.
Bowling: Mortaza 10-0-56-1, Hasan 8-0-62-0, Rahman 9-0-51-0, Sarkar 2-0-13-0, Hossain 7.2-0-47-0, Rubel 10-0-64-0, Rahman 1-0-13-1.
For South Africa, top of the International Cricket Council ODI rankings, this was a timely victory. However, the pair could still find the boundary when needed, as Hales demonstrated when he smashed a six off Sabbir Rahman.
Woakes was part of a four-pronged pace attack after Adil Rashid was left out to deny Bangladesh much spin. Tamim bellowed his frustration, for which he may be punished. However, from then on in it was plain sailing for the hosts as partnerships of 159 between Alex Hales and Joe Root and then 143 between Root and captain Eoin Morgan saw the hosts home comfortably.
Morgan was thrilled to have started the tournament on a high, and said: “When the guys bat like that, it’s certainly a lot easier than it used to be”. The six came off Moeen Ali – an inside out lofted shot over long-off.
Root’s Yorkshire teammate Liam Plunkett claimed 4-59 from his 10-over allocation, including the pivotal wicket of century-maker Tamim, who clashed with Stokes after reacting to the Durham man’s sledging.