Durham opening bowler Graham Onions has been called up as a replacement and will join the England squad.
Gough, who turns 36 later this month, returned for the series after a year out of cricket and played a Twenty20 and the opening two games last week.
After the pace bowler suffered soreness, a scan today.
showed a bone stress reaction in his left shin, however, and ECB chief medical officer Dr Peter Gregory said he would have to rest for six weeks.
Darren Gough said: ''I'm obviously extremely disappointed that this injury has ruled me out of the England side, I was looking forward to a strong NatWest Series which could have helped my chances for the upcoming winter tours''.
Gough, England's most successful One-day bowler with 235 wickets, has been selected for the squad to go to India for the Champions Trophy next month and his participation now looks doubtful.
Pakistan, who beat England by seven wickets at Lord's yesterday, lead the six-match one-day series 1-0 after the first match was abandoned due to rain.