Prydie, whose fine form this season led to a Wales squad recall, pulled up with a hamstring injury while training with the national side on Tuesday, while Evans picked up a shoulder problem during the LV= Cup win over London Wasps on Saturday.
Evans was forced from the field in the 20-8 Anglo-Welsh victory and is expected to be sidelined for between four to six weeks, with Prydie facing a similar length of absence.
As well as meaning neither player will feature in as many as four RaboDirect PRO12 fixtures and the Amlin Challenge Cup double header with Bordeaux-Begles, Prydie won't be able to play for his country in the remaining two Dove Men Series autumn internationals.
"Tom has been in good form this season and was growing in confidence and it's disappointing that he picked up an injury because I am sure he would have been in line for selection for Wales against Tonga," said Dragons boss Lyn Jones.
"It's a shame because Tom was just getting his game back together and was starting to build. He's had a tough couple of years since being selected for Wales (he won the first of his five caps as an 18-year-old three seasons ago), that was maybe before he was ready and he struggled to live up to that."
A four-week spell on the sidelines would see Prydie and Evans return in time for the December 21 PRO12 clash with Connacht and Dragons fans will no doubt be desperate to see the duo back to top form for the festive double header with Cardiff Blues. The Dragons host their local rivals at Rodney Parade on Boxing Day, before travelling to the Arms Park on New Year's Day.
Newport Gwent Dragons' upcoming fixtures
Glasgow PRO12 (A), Friday Nov 22
Munster PRO12 (H), Friday Nov 29
Bordeaux-Begles ACC (H) Friday Dec 6
Bordeaux-Begles ACC (A) Thursday Dec 12
Connacht PRO12 (A) Friday Dec 21
Cardiff Blues PRO12 (H) Thursday Dec 26
Cardiff Blues PRO12 (A) Wednesday Jan 1
Bath Rugby ACC (H) 9/10/11/12 Jan
Rugby Mogliano ACC (A) 16/17/18/19 Jan