The 31-year-old suffered the injury after landing awkwardly following an overhead clearance during his side's 4-2 Premier League victory over Southampton in February.
Coloccini has been allowed to return to his native Argentina for a week to work with his national association's medical team but Newcastle boss Alan Pardew has reconciled himself to being without the defender for a significant length of 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."
In January, Coloccini stated his desire to leave Newcastle and return to his homeland for personal reasons, but ended up remaining at St James' Park.
Pardew has defensive cover in January signing Mapou Yanga-Mbiwa but Coloccini's injury remains a blow to the Magpies, who are still looking to put a healthy distance between themselves and the relegation zone.
Yanga-Mbiwa is likely to start alongside Steven Taylor in Thursday's Europa League last-16 first-leg game with Anzhi Makhachkala at the Luzhniki Stadium in Moscow.