The incident occurred when the two politicians were talking in a back room, news website AL.com reported.
Details on what started the fight were not immediately available.
Birmingham police said they expected a report to be released later on Tuesday.
See more of the biggest news scandals of 2015:
Biggest news scandals of 2015
Alabama mayor, councilor in hospital after brawl, both pressing charges
Millions of adulterers (and perhaps some who signed up just for the thrill) were explored this year when hackers made good on a promise to release the contact information of everyone on the notorious Ashley Madison cheating website. The names, credit card information and sexual preferences of millions were revealed in the big hack, including reality star Josh Duggar.
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Former Secretary of State Hillary Clinton spent a good amount of this year defending herself for using private email servers to conduct official State Department business. The story dominated headlines for months, with many opponents questioning potential security lapses along with her judgment for using the servers in the first place. Clinton herself has admitted it wasn't her smartest decision.
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The world now knows that New England Patriots quarterback Tom Brady prefers slightly deflated balls, thanks to Deflategate. The controversy began when the team was accused of improperly tampering with footballs used in the AFC Championship Game against the Indianapolis Colts. Months after winning Super Bowl XLIX, Brady was slapped with a four-game suspension over his role in the scandal, which was reversed in time for him to play.
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The U.S. Department of Justice indicted more than two dozen FIFA officials and prompted nine arrests in Switzerland on counts including racketeering and money laundering related to the 2018 and 2022 World Cup bids.