Hewitt – who has made 103 senior appearances for Dragons – sustained an ACL and MCL injury in the defeat at Rodney Parade.
The 26-year-old will now undergo surgery next week before starting his rehabilitation and recovery process.
Dean Ryan, Director of Dragons Rugby, said: “It’s incredibly disappointing news for Ashton who was playing some outstanding rugby for us.
“He will now undergo surgery early next week before starting his journey back from injury.
“We all send our best wishes to Ashton and wish him well with his recovery.”