Plunkett was called into the squad earlier in the week as cover for the injured Steven Finn but then suffered a thigh strain.
He had been due to play for England Lions in two 50-over matches against Pakistan A in the United Arab Emirates before heading to Johannesburg but had to pull out of Wednesday's match in Dubai.
The ECB said Plunkett would stay in the Emirates for the rest of that series.
He remains in the England Twenty20 squad for that two-match series against South Africa, providing he recovers from his injury.
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Broad, who grabbed six second innings wickets in the third test in Johannesburg to spur England to a series win, is the number one test bowler in the world but has not played an ODI since last year's World Cup.
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
