Richards, who will become a free agent at the end of the season, is 5-4 with a 3.66 ERA. He was given the option of having the surgery or taking a non-surgical approach and had been weighing the decision overnight.
This is the third straight season that Richards has dealt with an arm injury.
The right-hander had been limited to six starts each of the past two seasons. He missed most of 2016 due to a UCL injury and had biceps nerve irritation last year.
In 2016, he opted not to have surgery for the UCL, opting instead for stem-cell and platelet-rich plasma treatment.
Richards had made 16 starts this season, his most since 2015. He made his second start on Tuesday since returning from the 10-day disabled list because of a left hamstring strain.
He gave up three runs on four hits over 2 2/3 innings and left the game in the middle of an at-bat in the third inning against Seattle’s Nelson Cruz.
Associated Press contributed to this report.