In a statement issued Monday afternoon, Buck said he needs to "to focus more fully on other activities and opportunities, which require my full attention."
Elected to city council in 2005, Buck has over the past eight years served terms as mayor and mayor pro tem. Those positions are elected by a majority of council members.
"I have great appreciation for our city staff, for their service orientation and their dedication to keep Farmington safe, well groomed and a great place to live," Buck wrote. "The engagement of our citizens is an attribute of our city, which is a valuable and vital element in our quality and character. I am constantly amazed by what our volunteers accomplish on behalf of our charming city."
Citing his focus on economic development, Buck said he has been pleased with the projects underway.
"Much has been accomplished and more opportunities are coming to Farmington every day," he wrote. "This will continue to be my focus and the application of my energy through my final day of service as Mayor and beyond that day."
Candidates remaining in the race include incumbents Bill Galvin and Greg Cowley, Erica Reaves, Jeffery Scott and Matthew Christian Wayne.