The Sharks hooker and co-captain failed a head injury assessment late in Saturday night's 36-12 loss to South Sydney.
But Brailey was feeling alert and well immediately after fulltime and managed to front the post-match press conference, hopeful of having his HIA regraded on appeal this week.
As part of his return-to-play protocols, Brailey completed light, non-contact training on Monday and has had no recurring symptoms.
But AAP has been told Cronulla have opted against risking Brailey and will not seek an exemption to play him.
The 27-year-old will be omitted from the Sharks' team sheet on Tuesday afternoon.
The New South Welshman is expected to be fit and available if selected for a State of Origin debut in the series opener on May 27.
He will not have the chance to play before coach Laurie Daley names his Blues side on Monday morning.
Brailey's incredible streak would have ended at 158 games had he not been rested from Cronulla's last regular-season game before the 2020 finals series.
Prior to that, he had not missed a game since his 2019 rookie campaign.
Former Sharks and Gold Coast prop Luke Douglas holds the NRL-era record for most consecutive games with 215.
Cameron McInnes, journeyman Jayden Berrell and ex-Newcastle player Riley Jones are contenders to start at hooker for Cronulla on Friday night.
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