Stokes will also miss the first-half of the five-match series against Australia with a torn hamstring.
Woakes will be assessed this week to ascertain if he'll be fit for the Australia series, which starts on June 13.
"Chris Woakes has been ruled out of the Scotland ODI with tightness in his right quad", the statement said.
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He later picked up a side strain after bowling just one over in England's campaign opener at the Champions Trophy in 2017.
Woakes' injury, meanwhile, comes on the back of the premier all-rounder Ben Stokes's injury news.
It is to be noted that the Stokes has not taken to field against Australia since last year's Champions Trophy, missing an Ashes Test series, five-match ODI series and T20 tri-series also involving New Zealand after he was sanctioned by the European Central Bank following his alleged involvement in a street brawl in Bristol last September. Curran though has been impressive in his brief ODI stint with England, picking up 12 wickets from eight games, including a five-fer against Australia earlier this year.