Gough's efforts in helping England win the first Test against Australia have left him short of fitness.
The decision was made after discussions between Gough, Wayne Morton, the England and Yorkshire physio, and chief executive Chris Hassall. The county added that there had been no approach from the England team management asking for Gough to be rested.
Sussex are lodging an official complaint with the English Cricket Board following their farcical Sunday league defeat at Durham.
The county faced a revised target of 80 in four overs under the complex Duckworth-Lewis system after torrential rain caused a 100-minute delay to the match at Chester-le-Street.
Lee Crozier become the first Northumberland player for 20 years to take a hat-trick, his success coming during the drawn Minor Counties' championship game with Norfolk.