The streak came to an end as Griffin grounded out in the sixth inning after walking in his second plate appearance during the Mobile BayBears' 6-5 loss to the Tennessee Smokies on Thursday.
The major league record is four straight at-bats with a home run, accomplished many times but last done by Carlos Gonzalez in 2012.
On Wednesday night, Griffin matched the Southern League record with four home runs in Mobile's 17-7 victory over the Smokies.
Griffin was 5-for-6 with seven RBIs on Wednesday. The 25-year-old first baseman hit solo homers in the fifth and sixth innings, added a three-run shot in the seventh, and had a two-run homer in the ninth. He also singled in the first.
Through Wednesday, the 6-foot-6 Griffin had nine homers in 40 games this season after hitting three in 61 games last season for Mobile. He played at Central Florida and was drafted in the 21st round by the Diamondbacks in 2011.
George Kalafatis had the only other four-homer game in Southern League history, accomplishing the feat for Montgomery in a 13-0 victory over visiting Birmingham on July 1, 1969.
The Associated Press contributed to this report.