He was set to skipper the Blues in their historic victory over reigning Heineken Cup champions Toulon last month but was forced to pull out at the last minute.
He underwent surgery last week and will now attend a specialist centre in Cardiff as he continues his treatment.
"Cardiff Blues have today confirmed that club captain Matthew Rees is to undergo further medical treatment that will extend his time away from the game," read a statement.
"The region announced last month that hooker Rees was to have an enforced spell away from rugby.
"Blues can now confirm that Rees will commence further treatment at Velindre Hospital, Cardiff from next week as he targets a return to playing in the future.
"Matthew has asked the region to pass on his sincere gratitude for the many messages he has received from well-wishers over the last two weeks and to thank the media for respecting his privacy at this time.
"The region will continue to support Matthew and his family in every way possible throughout this period and we look forward to his return to rugby in the future."
It is not known how long Rees, who has made 57 European appearances, will be sidelined.
The Blues face Glasgow Warriors in back-to-back matches in Rounds Three and Four of the Heineken Cup, beginning at the Arms Park on December 6.
They are currently sat at the bottom of Pool One but all is to play for with just one point separating them and group leaders Exeter.