Mr Dixon also served on the Alabama Board of Medical Examiners.
A close friend told NBC News that his last words to his wife were also a warning to the people of Alabama.
Dr David Thrasher said Mr Dixon told his wife Gaynell: “We messed up, we let our guard down.”
“Please tell everybody to be careful. This is real, and if you get diagnosed, get help immediately.”
According to Dr Thrasher, Mr Dixon believes he was exposed to the virus at an outdoor event two weeks ago. Two other attendees have since tested positive.
Early symptoms set in a few days after the event, and when they worsened Mr Dixon was placed on a ventilator. He passed away on 4 December.
Mrs Dixon also tested positive for Covid-19 last week and is recovering. Both of their daughters were ill with the coronavirus earlier in the year, but recovered and have not been reinfected.
Before his retirement in 2010, Mr Dixon served as state senator for Alabama Senate District 25, covering Montgomery, Ellmore, and Crenshaw counties. He took up the seat in 1983 having served four years on in the state House of Representatives, and three years on the Montgomery City Council.
Former colleagues paid tribute to him a great legislator who devoted his life to service of his adopted city of Montgomery.
In a statement, the Board of Medical Examiners said: “While we mourn Larry Dixon’s passing, we are forever grateful for his distinguished service to the medical profession and to the State of Alabama. He set an incredible example of service for us all. Our thoughts and prayers are with his wife, Gaynell, and his family during this difficult time.”
Mr Thrasher said that Mr Dixon was the “finest human being”, demonstrated by his last wish being to prevent more people from suffering from the same fate.
“He wanted to encourage people to be careful, wear a mask, don’t socially gather,” Mr Thrasher said. “He said, ‘Let’s save some lives.’”
By Monday, Alabama had recorded more than 270,000 confirmed cases of Covid-19, and the official death toll stood at 3,889, according to figures compiled by The New York Times.
Nationally, the number of cases stands at 14.8 million with more than 282,000 deaths.