Spencer collided with Auckland team-mate Daniel Braid at a Blues training session and is unlikely to return until their Super 12 clash against the Hurricanes on May 6.
The New Zealand international, who will be hoping to face the British & Irish Lions this summer, is expected to have an operation on Saturday to plate and repair the damage.
Spencer has endured a torrid season so far after being relegated to the bench in favour of the up-and-coming Tasesa Lavea.
Spencer, who has played 96 games for the Blues, suffered a similar facial injury last year when his jaw was broken while playing against the Chiefs.
He recovered in time for the All Blacks early season Tests and the Tri-Nations series.