The shot would have gone to Assuncao, but he was unable to accept having suffered an injury in his most recent bout.
Assuncao is currently riding a six-fight victorious streak, including the October 2013 win over Dillashaw, but suffered a rib injury when he defeated Pedro Munhoz at UFC 170 in February.
He does, however, expect to be waiting as the next challenger for whoever wins the bout between Barão and Dillashaw.
“Due to a rib injury and not being released by doctors, I couldn't take the opportunity to fight for the belt at UFC 173 on May 24,” Assuncao wrote in Portuguese on his Facebook page on Friday.
“I will be in preparation, waiting for my chance to be the next challenger. I'm totally focused and believe when the time comes I'll be ready, not only to fight, but to be the new champion.”
The opportunity for Barão and Dillashaw to headline UFC 173 came about earlier this week when middleweight champion Chris Weidman opted for surgery to repair lingering knee injuries. Weidman was slated to put his belt on the line against Lyoto Machida. The two will now fight at UFC 175 in July.
With Assuncao sidelined, Dillashaw was pulled from his feature bout against Takeya Mizugaki to face Barão.
UFC 173 takes place on May 24 at the MGM Grand Garden Arena in Las Vegas.