Stokes, who was replaced in England's team for the second Test by 19-year-old all-rounder Sam Curran, was sent for a scan on Thursday afternoon that revealed the tear in his left hamstring.
But the skipper is expected to be fit to face Scotland this weekend and for the beginning of the five-match ODI series against Australia beginning at The Oval on 13 June.
England allrounder Chris Woakes has been ruled out of the Scotland ODI with tightness in his right quad.
England are also slated to play a one-off ODI against Scotland in Edinburgh on June 10 before they will head to Australian series. The Joe Root-led side went on to win the game by an innings and 55 runs and levelled the two-match series 1-1.
The statement added: "Stokes, who sustained the injury in the build-up to the Test match at Headingley against Pakistan, will be assessed later this week".