He brought his hundred up off 42 balls as Bears made 242-4 and bowled out Derbyshire for 182 to win by 60 runs.
The New Zealand captain hit 11 sixes and 13 fours in the second highest T20 score ever, behind Chris Gayle's 175 in the Indian Premier League in 2013.
The previous T20 Blast record was 153, by Luke Wright for Sussex in 2014.
McCullum has hit 158 not out before, for the Kolkata Knight Riders in the first ever IPL game in 2008, an innings that took 73 balls.
The 33-year-old led New Zealand to a 1-1 draw in the recent Test series against England, before the Kiwis were beaten 3-2 in the subsequent one-day international series.
Birmingham Bears' Brendon McCullum smashed 158 not out off 64 balls against Derbyshire at Edgbaston, the highest ever T20 Blast score.