The 31-year-old central defender broke two bones in his back after landing awkwardly as he made a spectacular overhead clearance during his side's 4-2 Barclays Premier League victory over Southampton on February 24.
Coloccini has been allowed to return to his native Argentina for a week to work with his national association's medical team, but Pardew is expecting him to be sidelined for some time.
The manager said: "Colo has gone back to Argentina. There's no treatment he can have - he's broken two of the bones in his back.
"We think it's going to be anything between three and seven weeks. He's gone back for a week."