Potter wrote a letter Tuesday to Mayor Mike Elliott, Acting City Manager Reggie Edwards and Police Chief Tim Gannon ... saying, "I have loved every minute of being a police officer and serving this community to the best of my ability, but I believe it is in the best interest of the community, the department, and my fellow officers if I resign immediately."

Mayor Elliott announced Chief Gannon is also stepping down.

The resignations come following the second night of unrest in Minnesota that included looting, clashes with police and arrests. As we reported, citizens took to the streets Monday night in the Minneapolis suburb of Brooklyn Center ... gathering outside the police station to demand justice.

There had been a 7 PM curfew set in place but the streets remained flooded with protesters. Cops ultimately dispersed the crowd with flash bombs and chemical agents. Protesters also got violent ... launching objects at cops.

The protests came after 20-year-old Wright was shot and killed by Potter ... whose body cam footage shows her yelling "Taser" as she clearly was holding her handgun. She fired one round that ultimately killed Wright. You can also hear Potter on body cam footage saying, "S**t, I just shot him."