Officers say two men, whom they believe were wearing balaclavas, broke into the golf academy shop, before making off with a "four figure sum" of equipment.
The break-in occurred on Friday at 10.25pm.
The pair drove along the A823 in a small silver car before turning into Station Road to get to the course, leaving using the same route.
One of the suspect is described as wearing dark jeans, a black jacket and brown shoes, while the other is said to have been wearing blue jeans, a black jacket and light coloured trainers.
Constable Jack Stirling said: "I am appealing to anyone who was in the Gleneagles area between 10pm and 10.30pm on Friday to get in touch if they saw or heard anything suspicious.
"The A823 was busy at that time with numerous cars travelling along the road.
"Perhaps you saw a car driving or people within behaving suspiciously?
"If you have any dash-cam footage that you believe could assist with our investigation, please come forward as soon as possible."
"If you have any information in connection with the break-in, no matter how small you think it is, you can contact police on 101, quoting incident number 4088 of 17 January. You can also contact the independent charity Crimestoppers on 0800 555111 which is 100% confidential."