The Canadian driver was diagnosed with a concussion on Saturday when he was hit in the head with debris during the inaugural Grand Prix of Indianapolis.
IndyCar officials said Tuesday that Hinchcliffe was progressing well and had been cleared to begin light training. He will undergo another evaluation on Thursday.
E.J. Viso has replaced the Oakville, Ont., native as the Andretti Autosport team prepares for Indy 500 qualifying ahead of the May 25 race.