The injury compounded a miserable day for the Magpies, who had Mathieu Debuchy sent off and were beaten after conceding a late penalty.
Pardew said: "It has been a bad afternoon. Not only do we lose Debuchy but Colo also looks to have done something to his knee.
"It is early days but we could be looking at four to six weeks out."
Debuchy's dismissal for a two-footed challenge on Claudio Yacob came just three minutes before Argentinian centre-back Coloccini was forced off and changed the complexion of the game.
West Brom stepped up the pace and won with a Saido Berahino spot-kick after Tim Krul tripped Matej Vydra with four minutes remaining.