Medics decided the Sale fly-half should stay at home to speed up his recovery and reduce the risk of the virus sweeping through the squad.
England suffered badly during the recent tour of South Africa when a serious strain of gastro-enteritis left some players hospitalised.
However, Hodgson's symptoms are not thought to be as serious and it is hoped he will be fit to join his team-mates in training on the Algarve within a few days.
The majority of the 47-man squad flew out to Portugal on Thursday after spending three days in training with the Royal Marines.
Mike Tindall is continuing his rehabilitation from a broken leg in England, while Julian White has missed the trip for personal reasons.
But winger Jason Robinson, who underwent knee surgery following the South Africa tour, is taking part in selected elements of the conditioning programme in the Algarve.
Prop Andrew Sheridan is also continuing his rehabilitation programme in the Algarve as he recovers from knee ligament damage suffered in Sale's Anglo-Welsh Cup semi-final defeat to Leicester.