The 35-year-old free agent has been charged with making misdemeanour threats and disorderly conduct following the incident at Messinger Pinnacle Peak Mortuary on Monday.
US media reports said Incognito, who on Sunday confirmed on Twitter that his father had died, allegedly threatened staff at the funeral home and damaged property inside the business.
The former offensive lineman was one of the most controversial players in the NFL during his 11 seasons in the league, which also included a stint with the St. Louis Rams.
A series of on-field infringements saw him voted the "dirtiest player in the NFL" according to a 2009 poll in Sporting News.
In 2013, he was the central figure in a bullying scandal at the Dolphins involving team-mate Jonathan Martin, which eventually saw Incognito suspended for three months.
Incognito was later released by the Dolphins and sat out the 2014 season before being signed by the Buffalo Bills.
He was released by the Bills in May and soon afterwards was in trouble with authorities again, placed on an involuntary psychiatric hold for his involvement in an altercation at a gym in Boca Raton, Florida.