Murray, ranked No. 3 in the world, missed the French Open this spring after injuring his back during a tournament in Rome.
The 26-year-old from Scotland said in a statement that "the aim is to be fully fit for the new season."
Murray, who has dealt with lower back pain for the last two years, took to Twitter to thank his fans for their support.
Thanks so much for all the nice messages today... Having operation on monday.. Will let everyone know how it goes.. Ill be "back" stronger— Andy Murray (@andy_murray) September 19, 2013
Murray was bounced from the U.S. Open two weeks ago in the quarterfinals while trying to defend the title, losing 6-4, 6-3, 6-2 to Stanislas Wawrinka of Switzerland.
Murray then helped Britain defeat Croatia in Davis Cup group play last week with two victories in singles before deciding to undergo surgery.